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  • 1
    Electronic Resource
    Electronic Resource
    Affine-scaling for linear programs with free variables (1989)
    Springer
    Mathematical programming 43 (1989), S. 31-44 
    Details
    ISSN: 1436-4646
    Keywords: Affine-scaling ; Karmarkar's algorithm ; dual algorithm ; feasibility algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582276
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  • 2
    Electronic Resource
    Electronic Resource
    On ternary problems (1989)
    Springer
    Mathematical programming 45 (1989), S. 35-47 
    Details
    ISSN: 1436-4646
    Keywords: Facets ; ternary ; covering ; packing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider ternary matrices, i.e., integer matrices having all entries 0, 1 or 2. Three associated problems—the group problem, covering, and packing—are studied. General classes of vertices and facets are discussed in each case. Certain lifting procedures are also described. For all three problems techniques used are natural extensions of those used in the binary case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589095
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  • 3
    Electronic Resource
    Electronic Resource
    Some numerical experiments with variable-storage quasi-Newton algorithms (1989)
    Springer
    Mathematical programming 45 (1989), S. 407-435 
    Details
    ISSN: 1436-4646
    Keywords: 49D05 ; 65K05 ; Conjugate gradient ; diagonal updates ; Hilbert spaces ; large-scale problems ; limited memory ; numerical experiments ; unconstrained optimization ; variable-metric algorithms ; variablestorage
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes some numerical experiments with variable-storage quasi-Newton methods for the optimization of some large-scale models (coming from fluid mechanics and molecular biology). In addition to assessing these kinds of methods in real-life situations, we compare an algorithm of A. Buckley with a proposal by J. Nocedal. The latter seems generally superior, provided that careful attention is given to some nontrivial implementation aspects, which concern the general question of properly initializing a quasi-Newton matrix. In this context, we find it appropriate to use a diagonal matrix, generated by an update of the identity matrix, so as to fit the Rayleigh ellipsoid of the local Hessian in the direction of the change in the gradient. Also, a variational derivation of some rank one and rank two updates in Hilbert spaces is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589113
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  • 4
    Electronic Resource
    Electronic Resource
    Block truncated-Newton methods for parallel optimization (1989)
    Springer
    Mathematical programming 45 (1989), S. 529-546 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear optimization ; parallel computing ; block iterative methods ; truncated-Newton methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Truncated-Newton methods are a class of optimization methods suitable for large scale problems. At each iteration, a search direction is obtained by approximately solving the Newton equations using an iterative method. In this way, matrix costs and second-derivative calculations are avoided, hence removing the major drawbacks of Newton's method. In this form, the algorithms are well-suited for vectorization. Further improvements in performance are sought by using block iterative methods for computing the search direction. In particular, conjugate-gradient-type methods are considered. Computational experience on a hypercube computer is reported, indicating that on some problems the improvements in performance can be better than that attributable to parallelism alone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589117
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  • 5
    Electronic Resource
    Electronic Resource
    Numerical solution of ordinary and partial functional-differential eigenvalue problems with the Tau Method (1989)
    Springer
    Computing 41 (1989), S. 205-217 
    Details
    ISSN: 1436-5057
    Keywords: 65Q05 ; 65L15 ; 65N25 ; 65N35 ; Functional differential eigenvalue problems ; differential equations ; partial differential equations ; eigenvalues ; Tau Method ; collocation ; Legendre or Chebyshev series methods ; spectral Tau method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Mit Hilfe einer neuen Formulierung der Tau-Methode werden Eigenwertprobleme für gewöhnliche und partielle Funktional-Differentialgleichungen auf verallgemeinerte algebraische Eigenwertprobleme reduziert. Ein einfacher Algorithmus liefert genaue numerische Ergebnisse, die wir an Hand einiger konkreter Beispiele diskutieren. Zur weiteren Verbesserung der Ergebnisse wird Extrapolation verwendet.
    Notes: Abstract We apply a recent new formulation of the Tau Method to reduce the numerical treatment of eigenvalue problems for ordinary and partialfunctional-differential equations to that of generalized algebraic eigenvalue problems. We find accurate numerical results through the use of a simple algorithm which we discuss in applications to several concrete examples. Extrapolation is used to refine the results already obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02259093
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  • 6
    Electronic Resource
    Electronic Resource
    How to avoid logarithms in comparisons with uniform random variables (1989)
    Springer
    Computing 41 (1989), S. 163-166 
    Details
    ISSN: 1436-5057
    Keywords: Primary 65 C 10 ; Random variables ; acceptance-rejection ; logarithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Bei der Erzeugung nicht-gleichverteilter Zufallszahlen muß häufig der Logarithmus einer gleichverteilten Zufallszahl mit einer Testgröße verglichen werden. Es wird gezeigt, daß dieser Vergleich ohne den Aufruf einer Logarithmusroutine effizient durchführbar ist; zwei Prozeduren für diese Aufgabe werden vorgestellt und verglichen.
    Notes: Abstract In many algorithms for sampling from non-uniform distributions the logarithm of a uniform deviate must be compared with some test quantity. It is shown that all these comparisons can be done efficiently without calling a logarithm subprogram: two procedures for this task are presented and compared.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238740
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  • 7
    Electronic Resource
    Electronic Resource
    Order barriers for the B-convergence of ROW methods (1989)
    Springer
    Computing 41 (1989), S. 219-235 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; Numerical analysis ; stiff problems ; Rosenbrock methods ; B-convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden die Konvergenzeigenschaften der ROW-Verfahren bei ihrer Anwendung auf das steife Differentialgleichungsmodell von Prothero und Robinson untersucht. Dabei zeigt es sich, daß es Barrieren für die tatsächlich erreichbare Konvergenzordnung gibt. Ferner existieren ROW-Verfahren, deren Genauigkeit asymptotisch mit der Steifheit des Modells zunimmt. Die theoretischen Ergebnisse werden an numerischen Beispielen demonstriert.
    Notes: Abstract The convergence of ROW methods is studied when these methods are applied to the stiff model equation of Prothero and Robinson. It turns out that there are barriers of the attainable order of convergence. Furthermore, the existence of ROW methods is shown the accuracy of which increases asymptotically with the stiffness of the model. The theoretical results are demonstrated by numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02259094
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  • 8
    Electronic Resource
    Electronic Resource
    A numerical method for transmission problems for the Helmholtz equation (1989)
    Springer
    Computing 41 (1989), S. 267-274 
    Details
    ISSN: 1436-5057
    Keywords: 65R20 ; Integral equations ; transmission problems ; projection methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Verfahren besteht in der Entkopplung in zwei Randwertprobleme, welche mit bekannten Verfahren gelöst werden können. Der Konvergenzbeweis wird mit Hilfe der Integralgleichungsmethode und Konvergenzaussagen über Projektionsverfahren geführt.
    Notes: Abstract This method consists in decoupling the transmission problem into two boundary value problems, which can be solved separately by well known procedures. A convergence proof is given with the help of the integral equation method and convergence results on projection methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02259097
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  • 9
    Electronic Resource
    Electronic Resource
    Fast method to compute the scalar product of gradient and given vector (1989)
    Springer
    Computing 41 (1989), S. 261-265 
    Details
    ISSN: 1436-5057
    Keywords: 65V05 ; 65K10 ; 68C25 ; Automatic differentiation ; complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Arbeit behandelt ein spezielles Problem des Automatischen Differenzierens. Seif eine rationale Funktion vonn Variablen, sei #(f) die Anzahl der Operationen in der Auswertung vonf(x), seig der Gradient vonf. Viele Algorithmen zur Minimierung vonf(x) benötigen das Skalarproduktg(u) tv. In der Standardmethode zur Berechnung vong(u) tv wächst der Arbeitsaufwand mitn·#(f). In der vorliegenden Arbeit wird eine neue Methode zur Berechnung vong(u) tv angegeben. Die neue Methode erweist sich als wesentlich schneller, ihr Arbeitsaufwand wächst nur mit #(f).
    Notes: Abstract The paper deals with a special problem in Automatic Differentiation. Letf be a rational function ofn variables, let #(f) denote the number of operations to evaluatef(x), letg denote the gradient off. Many algorithms for minimizingf(x) require the scalar productg(u) tv. In the standard method for computingg(u) tv the amount of work grows withn·#(f). In this note a new method for computingg(u) tv is presented. The new method is considerably faster, its amount of work only grows with #(f).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02259096
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  • 10
    Electronic Resource
    Electronic Resource
    Characterization of B-convergent Runge-Kutta methods for strictly dissipative initial value problems (1989)
    Springer
    Computing 42 (1989), S. 61-67 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; Stiff initial value problems ; B-convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Auf der Klasse von Anfangswertproblemen mit negativer einseitiger Lipschitzkonstante ist die Eigenschaft algebraischer Stabilität eines Runge-Kutta-Verfahrens notwendig und hinreichend für dessenB-Konvergenz.
    Notes: Abstract The property of algebraic stability turns out to be a sufficient and necessary condition for a Runge-Kutta method to beB-convergent on the class of problems with a negative one-sided Lipschitz constant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243143
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  • 11
    Electronic Resource
    Electronic Resource
    A kernel system for iconic image processing (1989)
    Springer
    Computing 42 (1989), S. 91-108 
    Details
    ISSN: 1436-5057
    Keywords: 68B99 (Software) ; Image processing ; standardization ; system design ; Ada
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Im folgenden stellen wir einen Gestaltungsentwurf für ein ikonisches Bildverarbeitungssystem vor und beschreiben eine virtuelle Maschine, die die hierfür notwendigen Operationen realisiert. Es werden sowohl Datentypen als auch die charakteristischen Operationen der Bildverarbeitung diskutiert, und es werden Datenobjekte sowie Bildverarbeitungsoperationen formal definiert. Abschließend wird eine mögliche Implementation skizziert, die auf den generischen Konstrukten der Programmiersprache Ada basiert.
    Notes: Abstract We present a proposal for the design of a kernel system for iconic image processing operations and construct a virtual machine for image processing. The data structures and typical operations in the field of digital image processing are discussed. Furthermore, we give a formal definition of the operations and data objects required and describe one way to implement them by using the generic features of Ada.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02239741
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  • 12
    Electronic Resource
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    Safe bounds for the solutions of nonlinear problems using a parallel multisplitting method (1989)
    Springer
    Computing 42 (1989), S. 171-186 
    Details
    ISSN: 1436-5057
    Keywords: 65G10 ; 65H10 ; 65W05 ; CR: G. 1.0 ; G.1.5 ; Parallel methods ; nonlinear systems ; enclosures ; error bounds ; interval iterative methods ; multisplittings
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für gewisse Systeme nichtlinearer GleichungenF(x)=0 entwicklen wir ein Verfahren, welches iterativ enge untere und obere Schranken für die Nullstellen vonF berechnet. Das Verfahren beruht auf einem Multisplitting für bestimmte Matrizen und weist so in natürlcher Weise Parallelität auf. Wir geben Kriterien für die Konvergenz der Schranken gegen die Nullstellen an und untersuchen die Konvergenzgeschwindigkeit.
    Notes: Abstract For some systems of nonlinear equationsF(x)=0 we derive an algorithm which iteratively constructs tight lower and upper bounds for the zeros ofF. The algorithm is based on a multisplitting of certain matrices thus showing a natural parallelism. We prove criteria for the convergence of the bounds towards the zeros and we investigate the speed of convergence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02239746
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  • 13
    Electronic Resource
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    Guaranteed inclusions for the complex generalized eigenproblem (1989)
    Springer
    Computing 42 (1989), S. 225-238 
    Details
    ISSN: 1436-5057
    Keywords: 65G10 ; 65G05 ; 65H15 ; Generalized eigenproblem ; inclusion of solution ; guaranteed results ; error bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Methode zur Berechnung garantierter Schranken für die Lösung des komplexen allgemeinen Eigenproblems beschrieben. Die Methode erweitert einen ähnlichen Ansatz für allgemeine nichtlineare Gleichungssysteme in der Art, daß für den vorliegenden speziellen Fall weitgehende Folgerungen aus schwächeren Voraussetzungen gezogen werden können.
    Notes: Abstract A method is described which produces guaranteed bounds for a solution of the generalized complex eigenproblem. The method extends a similar approach for general systems of nonlinear equations to the special case of complex pencils, where under weaker assumptions stronger assertions can be proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02239750
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  • 14
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    Achieving tolerance proportionality in software for stiff initial-value problems (1989)
    Springer
    Computing 42 (1989), S. 341-352 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; Initial-value problems ; error control ; tolerance proportionality ; local extrapolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Toleranztreue wird als minimale Bedingung dafür erkannt, daß eine einheitliche Interpretation der vom Benutzer geforderten Genauigkeit bei der Lösung von Anfangswertaufgaben möglich ist. Es werden Ergebnisse angeführt, die zeigen, daß ein Code den lokalen Fehler pro Einheitsschritt kontrollieren muß, um Toleranztreue zu erreichen. In Mehrschritt-Codes kann dieser Effekt dadurch erreicht werden, daß ein Korrektor-Verfahren verwendet wird, das eine Ordnung genauer ist als das Prädiktor-Verfahren. Diese Strategie ist leicht anzuwenden und führt zu besserer Toleranztreue als die Strategie des lokalen Fehlers pro Schritt, die oft bei Software für steife Probleme verwendet wird. Numerische Ergebnisse wurden mit zwei Codes gewonnen, die auf die vorgeschlagene Strategie modifiziert wurden. Die Ergebnissezeigen, daß durch die Modifikation eine signifikante Verbesserung der Toleranztreue bei geringem zusätzlichen Aufwand erreicht werden kann.
    Notes: Abstract Tolerance proportionality is identified as a minimum requirement for a more uniform interpretation of the user's requested accuracy in software for the solution of initial-value problems. Results are quoted that show that a code must control the local error per unit step in order to achieve tolerance proportionality. This effect can be obtained in codes based on multistep formulas by using a corrector formula of one order higher than the predictor formula. This strategy is simple to implement and leads to better tolerance proportionality than the local error per step strategy often used in stiff software.Numerical results are obtained from two existing solvers that have been modified to use the proposed strategy. These results show that there is a significant improvement in tolerance proportionality in the modified codes at little extra cost over the original versions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243229
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  • 15
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    Numerische Berechnung extremaler Fundamentalsysteme für Polynomräume über der Vollkugel (1989)
    Springer
    Computing 43 (1989), S. 37-45 
    Details
    ISSN: 1436-5057
    Keywords: 65 D 05 ; 65 D 32 ; Interpolation on the ball ; cubature formulae
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract Extremal fundamental systems are nodal systems with a small Lebesgue-constant (≤dimension). An exchange algorithm for their calculation in case of polynomial interpolation over the unit ballB r is realized. ForB 3 and algebraic degree 6, a system consisting of 84 nodes and with a Lebesgue-constant 〈26 is documented, the corresponding cubature leading to a relative error of ≈10−8 in case of analytic functions.
    Notes: Zusammenfassung Extremale Fundamentalsysteme sind Knotensysteme mit kleiner Lebesgue-Konstante (≤Dimension). Hier wird ein Austauschalgorithmus zu ihrer Berechnung für die Polynominterpolation über der VollkugelB r konkretisiert. Für dieB 3 und den Polynomgrad 6 wird ein aus 84 Knoten bestehendes System mit Lebesgue-Konstanten 〈26 numerisch angegeben. Die zugehörige Kubatur führt bei analytischen Funktionen auf einen relativen Fehler ≈10−8.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243804
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  • 16
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    Interval-majorant method and global optimization (1989)
    Springer
    Computing 43 (1989), S. 85-92 
    Details
    ISSN: 1436-5057
    Keywords: 65K10 ; 65G10 ; Global optimization ; guaranteed error bounds ; interval analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zur Bestimmung des globalen Maximums einer Funktion einer Veränderlichen auf einem abgeschlossenen Intervall [a, b] schlagen wir eine Intervall-Majoranten-Methode vor. Sie benützt die Vorteile und vermeidet die Nachteile zweier bekannter Verfahren. Numerische Resultate werden berichtet.
    Notes: Abstract For seeking the global maximum of a function of a single variable defined on a closed interval [a, b] an interval-majorant method is proposed. This method derives advantages and avoids defects from both the one-step strategy method and the interval method. Numerical results are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243808
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  • 17
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    Minimal cubature formulae of degree 2k−1 for two classical functionals (1989)
    Springer
    Computing 43 (1989), S. 141-157 
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    ISSN: 1436-5057
    Keywords: 65D32 ; 41A55 ; cubature formula ; ideal theory ; integration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es sind nur wenige Kubaturformeln bekannt, deren Knotenzahl Möllers unterer Schranke entspricht. In dieser Arbeit werden die Beziehungen zwischen reelen Idealen und Kubaturformeln ausgenutzt, um solche minimale Formeln mit beliebigem ungeraden Grad für zwei klassische Integrale zu bestimmen. Eine Basis der Ideale kann explizit angegeben werden, weiter können fast alle Knoten in geschlossener Form bestimmt werden. Es wird gezeigt, daß alle Knoten im Integrationsbereicht liegen.
    Notes: Abstract Cubature formulae with the number of nodes equal to Möller's lower bound are rare. In this paper, the relation between real polynomial ideals and cubature formulae is used to construct such minimal formulae of arbitrary odd degree for two classical integrals. We found general expressions for bases of these ideals and closed formulae for almost all nodes. We proved that all nodes are inside the domain of integration.
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    URL: http://dx.doi.org/10.1007/BF02241858
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  • 18
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    Editorial (1989)
    Springer
    AI & society 3 (1989), S. 1-2 
    Details
    ISSN: 1435-5655
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01892671
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  • 19
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    Human experts and expert systems: A view from the shop-floor (1989)
    Springer
    AI & society 3 (1989), S. 47-57 
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    ISSN: 1435-5655
    Keywords: Expert systems ; Skilled shop-floor work ; Maintenance ; Dialectics ; Cognitivism ; Intuitionism ; Expertise ; Mental operations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract For quite some time, the research in artificial intelligence has focused on expert systems, because here are to be found practical applications at the experimental stage which may soon become widespread. This focus makes more pressing the need to link the debate about the fundamental efficiency of artificial intelligence with those activities that aim at the application of specialized expert systems. In this paper, I begin by considering the stages and the development of human expertise. As a frame of reference I propose a polar dialectic model of the development of human acting and thinking that explicitly deals with the interplay of calculating rationality and intuition. This suggests the use of expert systems as decision aids particularly in the field of maintenance work on the shop-floor. With regard to this case, some theses concerning the human-centred shaping of technology and work are presented.
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    URL: http://dx.doi.org/10.1007/BF01892675
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  • 20
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    In search of the computer-aided craftsman (1989)
    Springer
    AI & society 3 (1989), S. 39-46 
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    ISSN: 1435-5655
    Keywords: Design of work and technology ; Empirical knowledge ; NC technology ; Shop floor programming ; System design
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Profound changes in world markets are resulting in conflict between traditional structures of production and new market requirements. The right answers to this challenge are heavily disputed. One option is to replace human work still further by artificially intelligent technology without changing basic structures of production. In contrast to this strategy, alternative production concepts seek to combine the unique human capabilities of perception, evaluation and decision making in unstructured situations with appropriately designed computer systems. Empirical evidence from the use of NC technology indicates that sensual experience and practical knowledge are necessary ingredients rather than disappearing residuals of efficient production. By far their tacit dimension does not allow complete transformation into objectified, scientific knowledge. In the field of metal cutting it is the skilled workers themselves who constitute the primary source of productivity. In order to overcome their traditionally problematic and uncomfortable working situation, shop-floor programming methods have been developed that are adapted to their concrete and graphic mode of thinking and acting. These allow workers to make their own efficient NC programs, thus maintaining their practical competence. This paper illustrates a necessary new perspective in system design: away from developing computer programs for imitating and replacing human expertise and towards designing computers as a useful tool for human experts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01892674
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  • 21
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    ... Cheep! (1989)
    Springer
    AI & society 3 (1989), S. 58-59 
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    ISSN: 1435-5655
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01892677
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  • 22
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    News section (1989)
    Springer
    AI & society 3 (1989), S. 73-77 
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    ISSN: 1435-5655
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01892681
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  • 23
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    Human-centred systems debate (1989)
    Springer
    AI & society 3 (1989), S. 79-79 
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    ISSN: 1435-5655
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01891318
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  • 24
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    Industrial cultural determinants of technological developments: Skill transfer or power transfer? (1989)
    Springer
    AI & society 3 (1989), S. 88-102 
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    ISSN: 1435-5655
    Keywords: Criteria for technology design ; Industrial culture ; Tacit knowledge ; Transfer of knowledge and skill
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper discusses the social effects resulting from the transfer of knowledge and skill both in the spheres of production and machine design. Relevant design determinants and their impact on technological developments are discussed within the theoretical framework of industrial cultures. Two types of skill transfer are analysed in connection with different production philosophies — one more Tayloristic, the other more workshop-oriented. Finally, the paper discusses the relation of both philosophies to the requirements of future production concepts.
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    URL: http://dx.doi.org/10.1007/BF01891320
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    The technological change of reality: Opportunities and dangers (1989)
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    AI & society 3 (1989), S. 117-132 
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    Keywords: Technological change of reality ; Intellectics ; Artificial intelligence ; Executive systems ; Legislative systems ; Executive sclerosis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This essay discusses the trade-off between the opportunities and the dangers involved in technological change. It is argued that Artificial Intelligence technology, if properly used, could contribute substantially to coping with some of the major problems the world faces because of the highly complex interconnectivity of modern human society. In order to lay the foundation for the discussion, the symptoms of general unease which are associated with current technological progress, the concept of reality, and the field of Artificial Intelligence are very briefly discussed. In the main body of the essay, the dangers are contrasted with the potential benefits of such high technology. Besides discussing more well-known negative and positive aspects we elaborate on the disadvantages of executive systems and the advantages of legislative systems. It is argued that only the latter might enable the re-establishment of the feedback-mechanism which proved so successful in earlier phases of evolution.
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    URL: http://dx.doi.org/10.1007/BF01891322
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    Decision making, computer attitudes and expert systems: What is our direction? (1989)
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    AI & society 3 (1989), S. 133-141 
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    ISSN: 1435-5655
    Keywords: Expert systems ; Decision making ; Attitudes ; Individual differences
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Expert systems have been concerned with applications dealing with medical diagnosis, mineral exploration, and computer configuration, with some efforts relatively successful in achieving results at least as good as human experts. Today, much is being written about these systems and managerial decision-making activities in organizations and the positive impact that they can have in these situations. However, it appears that expert systems could become somewhat of a panacea for some organizational ailments as research, development, and marketing of them continues at a fast pace. What may be forgotten in this technological thrust is the individual decision maker and his/her unique style of decision making which could affect acceptance and use of these systems. Another important consideration is the attitude people have toward computers and computer systems, which along with decision-making styles could certainly affect expert system effectiveness and ultimate success in organizations. This paper provides a discussion of potential problems that could occur regarding individual decision making and attitudes and their relationships to these systems.
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    URL: http://dx.doi.org/10.1007/BF01891323
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    On informatics and underdevelopment (1989)
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    AI & society 3 (1989), S. 146-155 
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    ISSN: 1435-5655
    Keywords: Informatics ; Development process ; Underdevelopment ; Self-reliance ; Social awareness ; Third World informaticians
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The main question in this article deals with the contribution of informatics to development. As an approach to an answer, it is pointed out in the first place, that there is not just one informatics and that “development” does not admit of only one definition. After delimiting the relevant concept of development, it is suggested that if informatics is to collaborate in its achievement it is essential to rely, in the Third World, on socially responsible technicians. Thus, the informatics of underdevelopment will attain the technical capacity and the political will required in order to assure a true concern for development.
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    Editorial (1989)
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    AI & society 3 (1989), S. 167-168 
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    Source: Springer Online Journal Archives 1860-2000
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    URL: http://dx.doi.org/10.1007/BF01891427
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    Automate or innervate? The role of knowledge in advanced manufacturing systems (1989)
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    AI & society 3 (1989), S. 198-208 
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    ISSN: 1435-5655
    Keywords: Automation ; Human-centred technology ; Systems design ; Propositional knowledge ; Practical knowledge
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This chapter examines the role of shopfloor knowledge in the operation of advanced manufacturing systems. Design trends towards full automation are contrasted with those toward hybrid, human-centred systems with particular emphasis on job design and the development and reproduction of knowledge. The chapter concludes with a short discussion of the problems inherent in hybrid design.
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    Ethical issues concerning expert systems' applications in education (1989)
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    AI & society 3 (1989), S. 209-219 
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    ISSN: 1435-5655
    Keywords: Ethics ; Expert Systems ; Education ; MYCIN ; GUIDON ; Intelligent CAI
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This article traces the connection between expert systems used as consultants in medicine and their design for instructional purposes in education. It is suggested that there are important differences between these applications. Recognizing these differences leads to the view that the development of intelligent computer-assisted instructions (ICAI) should be guided by empirical research into social/psychological consequences and by ethical inquiries into the acceptability of those consequences. Three proposals are put forward: (1) that the pedagogical role of intelligent CAI be clarified, (2) that forms of intelligent CAI be developed that aim primarily at refining rather than replacing human judgements, and (3) that ICAI research and development projects contain components which address ethical and social/psychological components and which are equitably-funded, integral parts of the overall development effort.
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    Limits to computation: The naive's guide to most of computing science! (1989)
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    AI & society 3 (1989), S. 234-246 
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    Source: Springer Online Journal Archives 1860-2000
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    URL: http://dx.doi.org/10.1007/BF01891434
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    News section (1989)
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    AI & society 3 (1989), S. 260-267 
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    URL: http://dx.doi.org/10.1007/BF01891437
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    What is a materials data system? (1989)
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    AI & society 3 (1989), S. 220-228 
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    ISSN: 1435-5655
    Keywords: Civilization ; Computerization ; Concepts of knowledge ; Data systems ; Meta-aspects ; Societal systems ; World history ; World picture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract During the last two decades considerable efforts have been made to develop computerized data systems for engineering materials. The results have not come up to the expectations of systems that can be used by designers for selecting of materials. Some factors have been recognized as responsible for the slow progress. It has proved difficult, however, for those involved in this development to make use of such information about the systems in question. Conflicts have occurred between different parties involved. It now seems that too little attention has been paid to the historical background of knowledge and systems related to civiliziation and society. A recently published review of world history from the point of view of the emergence of information technology has provided a basis for some considerations about the nature and roles of data systems. It can be shown that certain activities or features characterize each period of civilization and the development of computers and computerization should be considered as part of this sequence. The same is true for the world history of thinking and knowledge. In the present paper these historical considerations are combined with the observation that in their thinking and perception of ideas people appear to carry with them traditions from the past in varying degrees. Hence differences of opinion about the nature and roles of materials data systems may be explained by differences in the imprint of historical developments on people's ideas. In order to apply this lesson to the development of materials data systems, one has to learn also from the varying interpretations of world history that have been written through the ages. The best approach will probably be incremental and pragmatic rather than holistic and synoptic.
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    Law, liability and expert systems (1989)
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    AI & society 3 (1989), S. 169-183 
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    ISSN: 1435-5655
    Keywords: Expert system ; Professional ; Professional malpractice ; Product liability ; Intelligent knowledge based systems ; Artificial intelligence and law ; Computers and law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper examines some of the possible legal implications of the production, marketing and use of expert systems. The relevance of a legally useful definition of expert systems, comprising systems designed for use both by laymen and professionals, is related to the distinctions inherent in the legal doctrine underlying provision of goods and provision of services. The liability of the sellers and users of, and contributors to, expert systems are examined in terms of professional malpractice as well as product liability. A recurring theme indicates that legislators may be inclined to restrict possibilities of liability suits in order to avoid disincentives to the creation of expert systems.
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    URL: http://dx.doi.org/10.1007/BF01891428
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    Expert systems and computer-controlled decision making in medicine (1989)
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    AI & society 3 (1989), S. 184-197 
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    ISSN: 1435-5655
    Keywords: Expert systems ; Skill transfer ; Knowledge application ; Problem solving ; Interpretive processes ; Human-machine communication ; Decision-support
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The search for “usable” expert systems is leading somemedical researchers to question the appropriate role of these programs. Most current systems assume a limited role for the human user, delegating situated “decision-control” to the machine. As expert systems are only able to replace a narrow range of human intellectual functions, this leaves the programs unable to cope with the “constructivist” nature of human knowledge-use. In returning practical control to the human doctor, some researchers are abandoning focusedproblem-solving in favour of supportiveproblem-analysis. Using ONCOCIN and QMR as examples, this article contrasts these approaches and suggests that the latter avoids many of the difficulties currently facing medical expert systems.
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    URL: http://dx.doi.org/10.1007/BF01891429
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    An analogy between western legal traditions and approaches to artificial intelligence (1989)
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    AI & society 3 (1989), S. 229-234 
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    URL: http://dx.doi.org/10.1007/BF01891433
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    Offsets of curves on rational B-spline surfaces (1989)
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    Engineering with computers 5 (1989), S. 39-46 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract The construction of offset curves is an important problem encountered often in design processes and in interrogation of geometric models. In this paper the problem of construction of offsets of curves lying on the same parametric surface is addressed. A novel algorithm is introduced, whose main feature is the use of geodesic paths to determine points of the offset. The offset is then approximated in the underlying surface parameter space by B-splines interpolating data points obtained by traveling a known distance along the geodesics departing from corresponding points of the progenitor in a direction perpendicular to the latter. A comprehensive error checking scheme has been devised allowing adaptive improvement of the approximation of the offset. The applicability of the algorithm is demonstrated by number of numerical examples.
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    Factors that affect planning in a knowledge-based system for mechanical engineering design optimization with application to the design of mechanical power transmissions (1989)
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    Engineering with computers 5 (1989), S. 47-62 
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    ISSN: 1435-5663
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Intelligent computer-aided design (CAD) emulates the human activity of design so that production planning, decision making, and inventive design can be performed by computers. Based on the history of human experience in engineering design, a formalized and systematic approach to design should include procedures from (1) conceptual design, (2) layout design, and (3) numerical optimization. The highest level within such a system should be responsible for specifying and symbolically optimizing skeleton structures of generic (nonspecific) elements within the design process that are eventually to be specified uniquely (pinned down) and ultimately optimized numerically. Planning plays a key role in such a system. Planning has been utilized as a tool for process organization within the knowledge domains of chemical engineering, electrical engineering, manufacturing, as well as for general problem formulation and solution. State estimation, subtask scheduling, and constraint propagation have been found to be factors of prime importance in this type of problem. Problems associated with the implementation of a planning strategy within a knowledge-based system for mechanical engineering design optimization are discussed. A hypothesis for planning is put forth and examined within the context of a model of the mechanical design optimization process. An example that demonstrates the applicability of this approach to mechanical power transmission design is considered.
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    Object-oriented knowledge frameworks (1989)
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    Engineering with computers 5 (1989), S. 79-89 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract This paper introduces a strategy for the construction of object-oriented knowledge frameworks. Global control programs, which are traditionally used for manipulating structured representations, have been replaced by domain-specific resources. This new approach offers increased efficiency and simplified development of knowledge-based expert systems for problem domains that deal with a variety of complex structured information. A theoretical foundation is laid for the representation of knowledge, starting with the adoption of a simple schema for structuring stereotypical information. Data and method abstraction is achieved by installing knowledge frames into part of an object-oriented class system that supports procedural attachment and object communication. This allows frame specialization using domain-specific resources and subsequent construction of modular systems with these specialist frames. Editors are introduced for the alteration of data primitives used in declarative representation. Algorithms, which operate on these data primitives, are given for frame instantiation, data access, and user-directed inference. Examples from structural engineering are used throughout the paper to illustrate the practical application of object-oriented knowledge frameworks.
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    Improved optimum structural design by passive control (1989)
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    Engineering with computers 5 (1989), S. 13-22 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract The problem of optimum structural design by passive control is stated in a nonlinear programming form. A solution procedure, based on a successive selection of design and control variables, is presented. Neglecting the implicit analysis equations, the solution becomes independent of the control variables and a lower bound (LB) on the optimum can easily be obtained. The control variables are then selected to satisfy all constraints. If this cannot be achieved, the LB constraints are modified and the control variables are chosen for the revised optimal design. These two steps are repeated until the final optimum is reached. Employing the proposed procedure on various structural systems subjected to static loads showed that the final optimum has been achieved after a very small number of iteration cycles. The numerical examples illustrate a solution with two types of control devices: a linear spring device and a limited displacement device. It has been found that the final optimum is often identical or close to the initial LB solution. Savings of 14 to 63 percent in weight, compared with conventional optima without control, have been demonstrated for some common structures.
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    An expert system for field inspection of concrete dams: Part 1, engineering knowledge (1989)
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    Engineering with computers 5 (1989), S. 23-38 
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    ISSN: 1435-5663
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract This paper covers in more detail the material that was introduced in Ref. [1] and describes the final engineering reasoning and knowledge used for an expert system to assist during the field inspection of existing concrete dams. The knowledge base of this expert system was created by combining the traditional expert system approach with the reasoning procedures of qualitative physics. The traditional expert system approach was used to identify the shallow knowledge pertaining to the problem, and qualitative physics was used to identify the deep knowledge. The deep knowledge structured and organized the identification and representation of the shallow knowledge. The expert system uses shallow knowledge to combine a qualitative expert reasoning with a quantitative procedural evaluation of the stability of a dam. The present paper concentrates on the description of the engineering knowledge and Ref. [2] will concentrate on the artificial intelligence issues associated with the knowledge acquisition and representation associated with this expert system. The validation process compared results obtained by the expert system with those obtained by independent field inspection experts. Some of the results are presented here.
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    An expert system for setting time steps in dynamic finite element programs (1989)
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    Engineering with computers 5 (1989), S. 205-219 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract An expert system, ETUDES—Expert Time integration control Using Deep and Surface Knowledge System, which addresses the determination of the timestep for time integration of linear structural dynamic equations is described. This time-step may also be applicable for a moderately nonlinear simulation of the same structure. The program also determines whether an explicit or implicit method is most efficient for the particular simulation. A production rule programming system written in OPS5 is used for the implementation of this prototype expert system. Issues relating to the expert system architecture for this application, such as knowledge representation and structure, as well as domain knowledge are discussed. The prototype is evaluated by measuring it's performance in various benchmark model problems.
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    h andh-p version error estimation and adaptive procedures from theory to practice (1989)
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    Engineering with computers 5 (1989), S. 221-234 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract In this paper we introduce techniques that allow us to define a posteriori error estimators via well-known recovery techniques. These allow us to construct a posteriori error estimators for relatively general problems. Further, we introduce new adaptive procedures that make use of these estimators and, in particular, describe anh-p procedure that is simple to implement and that, as numerical experiments have shown, attains an accelerated rate of convergence expected from theh-p version.
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    Announcement (1989)
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    Engineering with computers 5 (1989), S. 259-259 
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
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    AnO(N) algorithm to automatically generate geometric triangulations satisfying the Delaunay circumsphere criteria (1989)
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    Engineering with computers 5 (1989), S. 177-193 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract This paper presents an algorithm for the generation of Delaunay triangulations for general nonmanifold geometric models. Octree concepts are used for point placement and providing the linear, with respect to the number of elements, growth rate of the algorithm. Compatibility and classification procedures are used in conjunction with point injection procedures to ensure that the final Delaunay triangulation is a geometric triangulation of the domain of interest.
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    Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation (1989)
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    Engineering with computers 5 (1989), S. 161-175 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract This paper describes a method for generating tetrahedral meshes. The algorithm, based on the Delaunay triangulation, can treat objects of essentially arbitrary complexity. In order to preserve the surface triangulation of solid objects, it is necessary to override the Delaunay property and redefine the triangulation when points are introduced that are close to solid boundaries. Details of this constrained Delaunay algorithm are presented and an efficient implementation of the triangulation method is described. Techniques for controlling the distribution of mesh points and tetrahedron quality are also discussed.
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    Knowledge-based control for finite element analysis (1989)
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    Engineering with computers 5 (1989), S. 195-204 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract This paper shows that control logic may be separated from analysis software and that a knowledge-based expert system can use this logic to perform interactive computation. Heuristics that control a simple interactive finite element analysis program are represented using a rule-based format and are used by a goal-driven logic processor to invoke analysis activity. Traditional algorithm-oriented control and the proposed knowledge-based control are compared in a simple displacement computation scenario to identify the advantages/disadvantages of the two approaches. General activities and constraints, practical methods of reasoning and representation, and knowledge-based expert systems are discussed with emphasis on applications to interactive finite element analysis. An analysis control expert system has been developed for use in the numerical analysis of two-dimensional linear problems in solid and structural mechanics. An example problem is used to clarify the methods used to direct activity and to identify the problems associated with conditional task processing for interactive analysis. The main difference between the analysis program described in this paper and conventional analysis programs is related to the control architecture. The general conclusion of this paper is that knowledge-based control is more effective and flexible than algorithm-oriented control.
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    Adaptive multiple-levelh-refinement in automated finite element analyses (1989)
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    Engineering with computers 5 (1989), S. 235-247 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract This paper discusses an automatic, adaptive finite element modeling system consisting of mesh generation, finite element analysis, and error estimation. The individual components interact with one another and efficiently reduce the finite element error to within an acceptable value and perform only a minimum number of finite element analyses. One of the necessary components in the automated system is a multiple-level local remeshing algorithm. Givenh-refinement information provided by an a posteriori error estimator, and adjacency information available in the mesh data structures, the local remeshing algorithm grades the refinement toward areas requesting refinement. It is shown that the optimal asymptotic convergence rate is achieved, demonstrating the effectiveness of the intelligent multiple-level localh-refinement.
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    A new approach to the analysis of random methods for detecting necessary linear inequality constraints (1989)
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    Mathematical programming 43 (1989), S. 97-102 
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    ISSN: 1436-4646
    Keywords: Random methods ; necessary constraints ; redundancy ; coordinate directions ; hypersphere directions ; linear inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A new approach is given for the analysis of random methods for detecting necessary constraints in systems of linear inequality constraints. This new approach directly accounts for the fact that two constraints are detected as necessary (hit) at each iteration of a random method. The significance of this two-hit analysis is demonstrated by comparing it with the usual one-hit analysis.
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    A result in surrogate duality for certain integer programming problems (1989)
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    Mathematical programming 43 (1989), S. 103-106 
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    Keywords: Integer programming ; surrogate duality ; duality gap ; equality constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider linear programming problems with some equality constraints. For such problems, surrogate relaxation formulations relaxing equality constraints existwith zero primal-dual gap both when all variables are restricted to be integers and when no variable is required to be integer. However, for such surrogate formulations, when the variables are mixed-integer, the primal-dual gap may not be zero. We establish this latter result by a counterexample.
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    Sublinear upper bounds for stochastic programs with recourse (1989)
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    Mathematical programming 43 (1989), S. 131-149 
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    ISSN: 1436-4646
    Keywords: Stochastic programming ; sublinear function ; simple recourse problem ; recourse model ; duality ; approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Separable sublinear functions are used to provide upper bounds on the recourse function of a stochastic program. The resulting problem's objective involves the inf-convolution of convex functions. A dual of this problem is formulated to obtain an implementable procedure to calculate the bound. Function evaluations for the resulting convex program only require a small number of single integrations in contrast with previous upper bounds that require a number of function evaluations that grows exponentially in the number of random variables. The sublinear bound can often be used when other suggested upper bounds are intractable. Computational results indicate that the sublinear approximation provides good, efficient bounds on the stochastic program objective value.
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    Conical projection algorithms for linear programming (1989)
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    Mathematical programming 43 (1989), S. 151-173 
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    ISSN: 1436-4646
    Keywords: Conical projection methods ; Karmarkar's LP algorithm ; linear programming ; poly-nomial-time algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Linear Programming Problem is manipulated to be stated as a Non-Linear Programming Problem in which Karmarkar's logarithmic potential function is minimized in the positive cone generated by the original feasible set. The resulting problem is then solved by a master algorithm that iteratively rescales the problem and calls an internal unconstrained non-linear programming algorithm. Several different procedures for the internal algorithm are proposed, giving priority either to the reduction of the potential function or of the actual cost. We show that Karmarkar's algorithm is equivalent to this method in the special case in which the internal algorithm is reduced to a single steepest descent iteration. All variants of the new algorithm have the same complexity as Karmarkar's method, but the amount of computation is reduced by the fact that only one projection matrix must be calculated for each call of the internal algorithm.
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    Successive column correction algorithms for solving sparse nonlinear systems of equations (1989)
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    Mathematical programming 43 (1989), S. 187-207 
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    ISSN: 1436-4646
    Keywords: Finite difference ; Jacobian ; nonlinear equation ; sparsity
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract This paper presents two algorithms for solving sparse nonlinear systems of equations: the CM-successive column correction algorithm and a modified CM-successive column correction algorithm. Aq-superlinear convergence theorem and anr-convergence order estimate are given for both algorithms. Some numerical results and the detailed comparisons with some previously established algorithms show that the new algorithms have some promise of being very effective in practice.
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    Degeneracy in infinite horizon optimization (1989)
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    Mathematical programming 43 (1989), S. 305-316 
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    Keywords: Sequential decision problems ; infinite horizon optimization ; forecast or solution horizons ; degeneracy ; perturbation ; near-optimal forecast horizon
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    Notes: Abstract We consider sequential decision problems over an infinite horizon. The forecast or solution horizon approach to solving such problems requires that the optimal initial decision be unique. We show that multiple optimal initial decisions can exist in general and refer to their existence as degeneracy. We then present a conceptual cost perturbation algorithm for resolving degeneracy and identifying a forecast horizon. We also present a general near-optimal forecast horizon.
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    Analysis of a class of fractional programming problems (1989)
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    Mathematical programming 43 (1989), S. 329-347 
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    ISSN: 1436-4646
    Keywords: Fractional programming ; c-programming
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    Notes: Abstract We propose a solution strategy for fractional programming problems of the form max x∈x g(x)/ φ(u(x)), where the functionφ satisfies certain convexity conditions. It is shown that subject to these conditions optimal solutions to this problem can be obtained from the solution of the problem max x∈x g(x) + λu(x), whereλ is an exogenous parameter. The proposed strategy combines fractional programming andc-programming techniques. A maximal mean-standard deviation ratio problem is solved to illustrate the strategy in action.
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    Quadratically constrained minimum cross-entropy analysis (1989)
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    Mathematical programming 44 (1989), S. 85-96 
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    ISSN: 1436-4646
    Keywords: Minimum cross-entropy ; maximum entropy ; information theory ; geometric programming ; duality theory
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    Notes: Abstract Quadratically constrained minimum cross-entropy problem has recently been studied by Zhang and Brockett through an elaborately constructed dual. In this paper, we take a geometric programming approach to analyze this problem. Unlike Zhang and Brockett, we separate the probability constraint from general quadratic constraints and use two simple geometric inequalities to derive its dual problem. Furthermore, by using the dual perturbation method, we directly prove the “strong duality theorem” and derive a “dual-to-primal” conversion formula. As a by-product, the perturbation proof gives us insights to develop a computation procedure that avoids dual non-differentiability and allows us to use a general purpose optimizer to find anε-optimal solution for the quadratically constrained minimum cross-entropy analysis.
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    Marginal values in mixed integer linear programming (1989)
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    Mathematical programming 44 (1989), S. 67-75 
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    ISSN: 1436-4646
    Keywords: Marginal values ; mixed integer programming
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    Topics: Computer Science , Mathematics
    Notes: Abstract For a given optimization problem, P, considered as a function of the data, its marginal values are defined as the directional partial derivatives of the value of P with respect to perturbations in that data. For linear programs, formulas for the marginal values were given by Mills, [10], and further developed by the current author [16]. In this paper, the marginal value formulas are extended to the case of mixed integer linear programming (MIP). As in ordinary linear programming, discontinuities in the value can occur, and the analysis here identifies them. This latter aspect extends previous work on continuity by the current author, [18], Geoffrion and Nauss, [5], Nauss, [11], and Radke, [12], and work on the value function of Blair and Jeroslow, [2]. Application is made to model formulation and to post-optimal analysis.
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    Referees 1988 (1989)
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    Mathematical programming 44 (1989), S. 123-125 
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    On the facial structure of the set covering polytope (1989)
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    Mathematical programming 44 (1989), S. 181-202 
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    Notes: Abstract Given a bipartite graphG = (V, U, E), a cover ofG is a subset $$D \subseteq V$$ with the property that each nodeu ∈ U is adjacent to at least one nodev ∈D. If a positive weightc v is associated with each nodev ∈V, the covering problem (CP) is to find a cover ofG having minimum total weight. In this paper we study the properties of the polytopeQ(G) ⊂ ℝ |V| , the convex hull of the incidence vectors of all the covers inG. After discussing some general properties ofQ(G) we introduce a large class of bipartite graphs with special structure and describe several types of rank facets of the associated polytopes. Furthermore we present two lifting procedures to derive valid inequalities and facets of the polytopeQ(G) from the facets of any polytopeQ(G′) associated with a subgraphG′ ofG. An example of the application of the theory to a class of hard instances of the covering problem is also presented.
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    Generalized edge packings (1989)
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    Mathematical programming 44 (1989), S. 235-245 
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    Keywords: Edge packing ; covering ; augmenting chain ; matching matroid ; odd chain packing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An extension of matchings is considered: instead of edges we use odd length chains all of which have distinct endpoints. We show that several properties of matchings can be extended to these packings: an augmenting chain theorem is given, several variations of packings are described and corresponding min-max results for bipartite graphs are stated. Relations with analogous covering problems are exhibited and we show that these packings generate matroids as in the matching case.
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    Open questions concerning Weiszfeld's algorithm for the Fermat-Weber location problem (1989)
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    Mathematical programming 44 (1989), S. 293-295 
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    ISSN: 1436-4646
    Keywords: Location theory ; The Fermat—Weber location problem ; Weiszfeld's iterative algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Fermat—Weber location problem is to find a point in ℝ n that minimizes the sum of the weighted Euclidean distances fromm given points in ℝ n . A popular iterative solution method for this problem was first introduced by Weiszfeld in 1937. In 1973 Kuhn claimed that if them given points are not collinear then for all but a denumerable number of starting points the sequence of iterates generated by Weiszfeld's scheme converges to the unique optimal solution. We demonstrate that Kuhn's convergence theorem is not always correct. We then conjecture that if this algorithm is initiated at the affine subspace spanned by them given points, the convergence is ensured for all but a denumerable number of starting points.
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    An implementation of Karmarkar's algorithm for linear programming (1989)
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    Mathematical programming 44 (1989), S. 297-335 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Karmarkar's algorithm ; interior point methods
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    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes the implementation of power series dual affine scaling variants of Karmarkar's algorithm for linear programming. Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested. Linear programs are expressed in an inequality form, which allows for the inexact computation of the algorithm's direction of improvement, resulting in a significant computational advantage. Implementation issues particular to this family of algorithms, such as treatment of dense columns, are discussed. The code is tested on several standard linear programming problems and compares favorably with the simplex codeMinos 4.0.
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    A cutting plane algorithm for a clustering problem (1989)
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    Mathematical programming 45 (1989), S. 59-96 
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    ISSN: 1436-4646
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    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we consider a clustering problem that arises in qualitative data analysis. This problem can be transformed to a combinatorial optimization problem, the clique partitioning problem. We have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope. These theoretical results are utilized in this paper. We describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before. We discuss some details of the implementation of our code and present our computational results. We mention applications from, e.g., zoology, economics, and the political sciences.
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    Solving combinatorial problems with combined Min-Max-Min-Sum objective and applications (1989)
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    Mathematical programming 45 (1989), S. 361-372 
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    Keywords: Combinatorial optimization ; matching and weighted matroid partition ; bicriterion analysis
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    Notes: Abstract The purpose of this paper is to introduce and study a new class of combinatorial optimization problems in which the objective function is the algebraic sum of a bottleneck cost function (Min-Max) and a linear cost function (Min-Sum). General algorithms for solving such problems are described and general complexity results are derived. A number of examples of application involving matchings, paths and cutsets, matroid bases, and matroid intersection problems are examined, and the general complexity results are specialized to each of them. The interest of these various problems comes in particular from their strong relation to other important and difficult combinatorial problems such as: weighted edge coloring of a graph; optimum weighted covering with matroid bases; optimum weighted partitioning with matroid intersections, etc. Another important area of application of the algorithms given in the paper is bicriterion analysis involving a Min-Max criterion and a Min-Sum one.
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    A tolerant algorithm for linearly constrained optimization calculations (1989)
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    Mathematical programming 45 (1989), S. 547-566 
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    Keywords: Convergence theory ; degeneracies ; linear constraints ; matrix factorizations ; nonlinear optimization ; semi-infinite programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Two extreme techniques when choosing a search direction in a linearly constrained optimization calculation are to take account of all the constraints or to use an active set method that satisfies selected constraints as equations, the remaining constraints being ignored. We prefer an intermediate method that treats all inequality constraints with “small” residuals as inequalities with zero right hand sides and that disregards the other inequality conditions. Thus the step along the search direction is not restricted by any constraints with small residuals, which can help efficiency greatly, particularly when some constraints are nearly degenerate. We study the implementation, convergence properties and performance of an algorithm that employs this idea. The implementation considerations include the choice and automatic adjustment of the tolerance that defines the “small” residuals, the calculation of the search directions, and the updating of second derivative approximations. The main convergence theorem imposes no conditions on the constraints except for boundedness of the feasible region. The numerical results indicate that a Fortran implementation of our algorithm is much more reliable than the software that was tested by Hock and Schittkowski (1981). Therefore the algorithm seems to be very suitable for general use, and it is particularly appropriate for semi-infinite programming calculations that have many linear constraints that come from discretizations of continua.
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    A numerical investigation of rank-two ellipsoid algorithms for nonlinear programming (1989)
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    Mathematical programming 43 (1989), S. 87-95 
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    Keywords: Ellipsoids ; nonlinear programming ; rank-two updates
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    Notes: Abstract We study the performance of some rank-two ellipsoid algorithms when used to solve nonlinear programming problems. Experiments are reported which show that the rank-two algorithms studied are slightly less efficient than the usual rank-one (center-cut) algorithm. Some results are also presented concerning the growth of ellipsoid asphericity in rank-one and rank-two algorithms.
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    New lower bounds for the Symmetric Travelling Salesman Problem (1989)
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    Mathematical programming 45 (1989), S. 233-254 
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    Keywords: Symmetric Travelling Salesman Problem ; additive bounding procedures ; reduced costs computation ; algorithms implementation
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    Notes: Abstract In this paper new lower bounds for the Symmetric Travelling Salesman Problem are proposed and combined in additive bounding procedures. Efficient implementations of the algorithms are given; in particular, fast procedures for computing the linear programming reduced costs of the Shortest Spanning Tree (SST) Problem and for finding all ther-SST of a given graph, are presented. Computational results on randomly generated test problems are reported.
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    Four problems on graphs with excluded minors (1989)
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    Mathematical programming 45 (1989), S. 311-330 
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    Notes: Abstract The four problems we consider are the Chinese postman, odd cut, co-postman, and odd circuit problems. Seymour's characterization of matroids having the max-flow min-cut property can be specialized to each of these four problems to show that the property holds whenever the graph has no certain excluded minor. We develop a framework for characterizing graphs not having these excluded minors and use the excluded minor characterizations to solve each of the four optimization problems. In this way, a constructive proof of Seymour's theorem is given for these special cases. We also show how to solve the Chinese postman problem on graphs having no four-wheel minor, where the max-flow min-cut property need not hold.
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    Valid inequalities and facets of the capacitated plant location problem (1989)
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    Mathematical programming 44 (1989), S. 271-291 
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    Keywords: Facets of polyhedra ; plant location ; capacitated fixed charge problems ; vertex packing
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    Notes: Abstract Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure. The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with a constant capacity for all plants. These facet inequalities depend on the capacity and thus differ fundamentally from the valid inequalities for the uncapacited version of the problem. We also introduce a second formulation for a model with indivisible customer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.
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    Operations research 1990, international conference operations research (1989)
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    Mathematical programming 44 (1989), S. 367-367 
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    Topics: Computer Science , Mathematics
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    On the set covering polytope: II. Lifting the facets with coefficients in {0, 1, 2} (1989)
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    Mathematical programming 45 (1989), S. 1-20 
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    Keywords: Set covering ; facet lifting ; polyhedral combinatorics
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    Notes: Abstract In an earlier paper (Mathematical Programming 43 (1989) 57–69) we characterized the class of facets of the set covering polytope defined by inequalities with coefficients equal to 0, 1 or 2. In this paper we connect that characterization to the theory of facet lifting. In particular, we introduce a family of lower dimensional polytopes and associated inequalities having only three nonzero coefficients, whose lifting yields all the valid inequalities in the above class, with the lifting coefficients given by closed form expressions.
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    The hirsch conjecture is true for (0, 1)-polytopes (1989)
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    Mathematical programming 45 (1989), S. 109-110 
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    Strong formulations for mixed integer programming: A survey (1989)
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    Mathematical programming 45 (1989), S. 173-191 
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    Keywords: Mixed integer programming ; strong formulations ; valid inequalities ; fiexd cost networks
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    Notes: Abstract We attempt to motivate and survey recent research on the use of “strong” valid inequalities and reformulation to solve mixed integer programming problems.
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    Multi-constrained matroidal knapsack problems (1989)
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    Mathematical programming 45 (1989), S. 211-231 
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    Keywords: Knapsack ; matroids ; asymptotically optimum bounds
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    Notes: Abstract We consider multi-constrained knapsack problems where the sets of elements to be selected are subject to combinatorial constraints of matroidal nature. For this important class of NP-hard combinatorial optimization problems we prove that Lagrangean relaxation techniques not only provide good bounds to the value of the optimum, but also yield approximate solutions, which are asymptotically optimal under mild probabilistic assumptions.
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    On the supermodular knapsack problem (1989)
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    Mathematical programming 45 (1989), S. 295-309 
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    Notes: Abstract In this paper we introduce binary knapsack problems where the objective function is nonlinear, and investigate their Lagrangean and continuous relaxations. Some of our results generalize previously known theorems concerning linear and quadratic knapsack problems. We investigate in particular the case in which the objective function is supermodular. Under this hypothesis, although the problem remains NP-hard, we show that its Lagrangean dual and its continuous relaxation can be solved in polynomial time. We also comment on the complexity of recognizing supermodular functions. The particular case in which the knapsack constraint is of the cardinality type is also addressed and some properties of its optimal value as a function of the right hand side are derived.
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    Systolic algorithms for computational geometry problems — A survey (1989)
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    Computing 41 (1989), S. 19-40 
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    ISSN: 1436-5057
    Keywords: Systolic algorithm ; computational geometry ; systolic array
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die neueren Entwicklungen, die zu parallelen Rechnerarchitekturen führen, haben die Aufmerksamkeit auf das Gebiet der parallelen “Computational Geometry” gelenkt. In diesem Artikel wird das Hauptaugenmerk auf systolische Algorithmen für diesen Themenkreis gerichtet. Es wird ein Überblick über derartige Algorithmen gegeben. Es zeigt sich, daß die meisten grundlegenden geometrischen Probleme mit eindimensionalen systolischen Arrays, wie sie von Kung et al. eingeführt wurden, in Linearzeit gelöst werden können. Eine Reihe neuer Ergebnisse wird vorgestellt, und offene Probleme werden angesprochen.
    Notes: Abstract With the recent development of a rich variety of parallel computer architectures, much attention has been paid to the study of parallel computational geometry. In this paper we put the focus on systolic computational geometry algorithms among those algorithms being developed rapidly in recent years for the various kinds of parallel processors. Our paper gives a survey of recent studies on systolic computational geometry algorithms We show that most of the fundamental geometrical problems can be solved in linear-time by conventional one-dimensional systolic arrays proposed by Kung et al. This paper also includes many new results and some open problems for which we have no linear-time systolic algorithms.
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    On the convergence of an iterative method for bounding the inverses of an interval matrix (1989)
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    Computing 41 (1989), S. 153-162 
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    Keywords: 65 G 10 ; Interval analysis ; matrix inversion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ein Iterationsverfahren zur Verbesserung einer Ausgangseinschließung für die Inversen einer Intervallmatrix wird vorgeschlagen. Für dieses wird eine Konvergenzaussage bewiesen mit hinreichenden Bedingungen an die Durchmesser der fraglichen Intervallmatrix und der Ausgangseinschließung, so daß das Verfahren eine Verbesserung bringt. Numerische Beispiele werden besprochen.
    Notes: Abstract An iterative method for improving an initial inclusion for the inverses of an interval matrix is [roposed. For this we prove a convergence theorem with sufficient conditions on the width of the interval matrix in question and of the initial inclusion so that our method yields an improvement. Numerical examples are discussed.
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    Strong stability results for the hopscotch method with applications to bending beam equations (1989)
    Springer
    Computing 41 (1989), S. 179-203 
    Details
    ISSN: 1436-5057
    Keywords: 65M10 ; 65M20 ; CR: G 1.8 ; Hopscotch method ; bending beam equation ; strong asymptotical stability ; three-term matrix-vector recursion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Hopscotch-Methode dient zur effizienten numerischen Integration von Systemen gewöhnlicher Differentialgleichungen, welche als Raumdiskretisierung aus zeitabhängigen partiellen Differentialgleichungen entstehen. Die Fortpflanzung des Integrationsfehlers durch die einzelnen Zeitschichten kann man durch eine dreistufige Rekursion beschreiben. Bei einem bestimmten Typ partieller Differentialgleichungen kann eine explizite und scharfe Schranke für den diskretenL 2-Fehler angegeben werden. Außerdem erhält man Bedingungen für die starke und die asymptotische Stabilität der Methode. Zudem ist das Stabilitätsverhalten gleichmäßig in Bezug auf die Raum- und die Zeitdiskretisierung. Diese neuen Bedingungen beschreiben die Stabilität der Hopscotch-Methode in den meisten Anwendungsfällen. Sie gegen weit über den Anwendungsbereich früherer Stabilitätsbedingungen hinaus.
    Notes: Abstract The hopscotch method is a numerical integration method that can be applied efficiently to the system of ordinary differential equations arising by space-discretization of time dependent partial differential equations (PDEs). The error propagation of this method from one time level to another can be described by a three-term matrix-vector recursion. In regards to PDEs that relate to (multi-dimensional) bending beam equations, we obtain an explicit sharp bound for the discreteL 2-norm of the propagated error. This bound is expressed in quantities determined by spectral properties of the matrices in the recursion. The expression leads to conditions under which the hopscotch method is strongly asymptotically stable: that is, the stability is uniform with respect to the mesh widths in space and time (that correlate and that tend to 0) and to the time level (that tends to ∞). In many applications, our conditions completely describe the situation in which the hopscotch method is strongly asymptotically stable. Previously known stability conditions are more restrictive and do not give complete descriptions.
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    Regularization and computation of a bifurcation problem with corank 2 (1989)
    Springer
    Computing 41 (1989), S. 307-316 
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    ISSN: 1436-5057
    Keywords: Primary 65H ; secondary 47E ; Bifurcation point ; extended system ; discretization ; Newton-like methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die numerische Approximation eines Verzweigungsproblems mit Korang 2 wird hier behandelt. In der Umgebung des Verzweigungspunktes wird die nichtlineare Gleichung in ein erweitertes System eingebettet. Die reguläre Lösung dieses Systems, die den Verzweigungspunkt und den Nullraum des entsprechenden Ableitungsoperators enthält, erlaubt die näherungsweise Berechnung von Verzweigungspunkt und Nullraum von allgemeinen Diskretisierungsmethoden und Newton-ähnlichen Verfahren. Anschließend werden numerische Beispiele diskutiert.
    Notes: Abstract This paper deals with a numerical approximation of a bifurcation problem with corank 2. In the neighborhood of the bifurcation point the nonlinear equation is embedded into an extended system. The regular solution of this system including bifurcation point and null space of the corresponding operator derivative allows approximate computation of the bifurcation point and the null space via general discretization and Newton-like methods. In addition, numerical examples are discussed.
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    URL: http://dx.doi.org/10.1007/BF02241220
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    The AOR method for solving linear interval equations (1989)
    Springer
    Computing 41 (1989), S. 359-364 
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    ISSN: 1436-5057
    Keywords: 65G10 ; 65H10 ; Linear interval equations ; AOR method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Diese Arbeit ist durch die Arbeit [7] motiviert, wo das SOR-Verfahren zur Lösung von linearen Intervallgleichungen betrachtet wird. Es ist bekannt, daß das AOR-Verfahren für lineare (“Punkt”) Gleichungssysteme manchmal schneller als das SOR-Verfahren konvergiert. Wir geben einige hinreichende Konvergenzbedingungen für das Intervall-AOR-Verfahren für dieselbe Klasse von Matrizen, die in [7] betrachtet wurde.
    Notes: Abstract This paper is motivated by the paper [7], where the SOR method for solving linear interval equations was considered. It is known that sometimes the AOR method for systems of linear (“point”) equations converges faster than the SOR method. We give some sufficient conditions for the convergence of the interval AOR method for the same class of interval matrices which are considered in [7].
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    Domain decomposition method for elliptic mixed boundary value problems (1989)
    Springer
    Computing 42 (1989), S. 45-59 
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    ISSN: 1436-5057
    Keywords: 65N20 ; 65F05 ; 65F10 ; Domain decomposition ; iterative methods ; substructures ; finite elements ; elliptic equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Methode zur Lösung elliptischer Probleme zweiter Ordnung mit gemischten Randbedingungen diskutiert. Das Finite-Elemente-Problem wird in Teilprobleme aufgespalten. Daraus resultieren Unterprobleme, welche auf die durch die Aufteilung entstehenden Teilgebiete bezogen sind, sowie ein Hilfsproblem, das mit den Trennkurven zusammenhängt. Die Unterprobleme werden direkt gelöst, das Hilfsproblem wird mittels einer Konjuguerten-Gradienten-Methode behandelt. Die Konvergenzgeschwindigkeit der KG-Methode wird auch für den Fall analysiert, daß Neumann und Dirichlet Randbedingungen auf Punkten der Trennkurven wechseln. Numerische Erfahrungen liegen vor.
    Notes: Abstract A method for solving the elliptic second order mixed boundary value problem is discussed. The finite element problem is divided into subproblems, associated with subregions into which the region has been partitioned, and an auxiliary problem connected with intersect curves. The subproblems are solved directly, while the auxiliary problem is handled by a conjugate gradient method. The rate of the convergence of the cg-method is discussed also for the cases when the Neumann and Dirichlet boundary conditions change at points belonging to the intersecting curves. Results from numerical experiments are also reported.
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    Linearly constrained optimization (1989)
    Springer
    Computing 42 (1989), S. 85-89 
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    ISSN: 1436-5057
    Keywords: 90C30 ; 63-04 ; Linearly constraints ; optimization conjugate directions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zur Lösung von Optimierungsproblemen mit linearen Restriktionen wird ein Algorithmus auf der Grundlage konjugierter Gradienten vorgestellt. Einige Testbeispiele zeigen hervorragendes Konvergenzverhalten.
    Notes: Abstract For linearly constrained optimization problems an algorithm is presented which is based on conjugate gradients. Numerical tests demonstrate a favourable behaviour of the new algorithm.
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    An alias method for sampling from the normal distribution (1989)
    Springer
    Computing 42 (1989), S. 159-170 
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    ISSN: 1436-5057
    Keywords: Primary 65C10 ; Random numbers ; normal distribution ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die effizientesten Algorithmen für Stichproben von der Standardnormalverteilung benötigen lange Listen von Konstanten. Die Größe dieser Tafeln wächst mit der verwendeten Präzision. Durch eine Anpassung der “Aliasmethode” von A.J. Walker an die Normalverteilung wird eine Stichprobenprozedur entwicklet, die nur drei feste Tafeln von je 128 Bytes braucht. Die neue Methode ist ebenso schnell wie ihre Konkurrenten und leichter zu implementieren.
    Notes: Abstract The most efficint algorithms for sampling from the standard normal distribution require long lists of constants. The size of these tables grows with the employed precision. By adapting A.J. Walker's “alias method” to the normal distribution a sampling procedure is developed which needs only three fixed tables of 128 bytes each. The new method is as fast as its competitors and easier to implement.
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    The treatment of integral equations with discontinuous kernels using product type quadrature formulas (1989)
    Springer
    Computing 42 (1989), S. 207-223 
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    ISSN: 1436-5057
    Keywords: 65R05 ; 45B05 ; CR5.18 ; Intergral equation ; discontinuous kernel ; quadrature method ; Green's function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Untersucht werden lineare Fredholmsche Integralgleichungen zweiter Art mit Kernen, die entlang beliebiger stetiger Kurven mit Unstetigkeiten behaftet sind. Zur Lösung werden Quadraturen vom Produkttyp (Boland-Quadraturen) in verallgemeinerter Form benutzt. Es werden eine allgemeine Konvergenztheorie entwickelt und spezielle Techniken vorgestellt sowie konkrete Quadraturformeln zur Lösung solcher Gleichungen angegeben. Das Verfahren wird anhand numerischer Beispiele demonstriert.
    Notes: Abstract Linear Fredholm integral equations of the second kind with kernels which are discontinuous along one or more continuous curves are considered. This paper discusses the use of generalized product type quadrature formulas (Boland quadrature formulas). A general convergence theory is developed and special techniques and quadrature formulas are given. The method is demonstrated on a numerical example.
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    Solving linear least squares by orthogonal factorization and pseudoinverse computation via the modified Huang algorithm in the ABS class (1989)
    Springer
    Computing 42 (1989), S. 195-205 
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    ISSN: 1436-5057
    Keywords: 65F05 ; Linear least squares ; QR method ; Moore-Penrose pseudoinverse ; ABS methods ; modified Huang algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir betrachten drei Algorithmen zur Lösung des linearen Ausgleichsproblems auf der Basis des modifizierten Huang-Algorithmus (MHA) in der Klasse ABS, die kürzlich für lineare Systeme von Abaffy, Broyden und Spedicato eingeführt wurde. Der erste Algorithmus benützt eine explizite QR-Faktorisierung der KoeffizientenmatrixA, die durch die Anwendung von MHA aufA T berechnet wird. Der zweite und der dritte Algorithmus bauen auf zwei Darstellungen der Moore-Penrose-Pseudoinversen auf, die mit Hilfe von MHA gewonnen werden. Alle drei Algorithmen werden an einem großen Satz von Beispielen getestet und mit dem NAG-Code verglichen, der eine QR-Faktorisierung mit Householder-Rotationen verwendet. Der Vergleich zeigt, daß die Algorithmen, die auf MHA aufbauen, im allgemeinen eine höhere Genauigkeit liefern.
    Notes: Abstract We consider three algorithms for solving linear least squares problems based upon the modified Huang algorithm (MHA) in the ABS class for linear systems recently introduced by Abaffy, Broyden and Spedicato. The first algorithm uses an explicit QR factorization of the coefficient matrixA computed by applying MHA to the matrixA T . The second and the third algorithm is based upon two representations of the Moore-Penrose pseudoinverse constructed with the use of MHA. The three algorithms are tested on a large set of problems and compared with the NAG code using QR factorization with Householder rotations. The comparison shows that the algorithms based on MHA are generally more accurate.
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    Splitting iteration method for simple singular points and simple bifurcation points (1989)
    Springer
    Computing 41 (1989), S. 87-96 
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    ISSN: 1436-5057
    Keywords: 65J15 ; 47H15 ; Singular point ; bifurcation point ; splitting iteration method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird ein iteratives Splitting-Verfahren zur Berechnung von einfachen singulären Punkten und von einfachen Verzweigungspunkten von nichtlinearen Gleichungen vorgestellt. Die Methode benötigt wenig Rechenaufwand und konvergiert mit einer regulierbaren Geschwindigkeit. Numerische Beispiele werden präsentiert.
    Notes: Abstract A splitting iteration method is introduced to compute the simple singular points and the simple bifurcation points of nonlinear problems. It needs little computational work and converges with an adjustable rate. Numerical examples are presented.
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    URL: http://dx.doi.org/10.1007/BF02238731
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    Implementing Brown's method for systems of nonlinear equations with dense banded Jacobian (1989)
    Springer
    Computing 41 (1989), S. 123-129 
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    ISSN: 1436-5057
    Keywords: 65H10 ; Brown's method ; banded systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir zeigen, daß das Brown-Verfahren in einer Weise implementiert werden kann, die besonders effizient ist, wenn man ein nichtlineares Gleichungssystem zu lösen hat, dessen Jacobi-Matrix voll besetzte Bandstruktur aufweist. Der arithmetische Aufwand für einen Iterationsschritt ist dann im wesentlichen so groß wie der Aufwand beim Gaußalgorithmus zur Lösung linearer Gleichungssysteme mit voll besetzter Bandmatrix.
    Notes: Abstract We show that Brown's method can be implemented in a manner that is particularly efficient if one wants to solve a system of nonlinear equations with dense banded Jacobian. The arithmetic work required for one iteration step is then essentially the same as the arithmetic work required to solve a dense banded linear system by Gaussian elimination.
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    New condition numbers for matrices and linear systems (1989)
    Springer
    Computing 41 (1989), S. 167-169 
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    ISSN: 1436-5057
    Keywords: 15 A 12 ; 65 F 35 ; 65 G 10 ; Condition numbers ; relative errors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Neue Konditionszahlen für Matrizen und lineare Gleichungssysteme werden eingeführt, die auf der Abhängigkeit der relativen Fehler des Resultats von den relativen Datenfehlern basieren.
    Notes: Abstract New condition numbers for matrices and linear systems are proposed, based on the dependence of the relative errors in the result upon the relative errors of the data.
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    Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems (1989)
    Springer
    Computing 42 (1989), S. 271-289 
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    ISSN: 1436-5057
    Keywords: 90C30 ; Constrained global optimization ; concave minimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zur Lösung konkaver Minimierungsprobleme sind einige (theoretische) Verfahren vorgeschlagen worden; wenig ist über ihr numerisches Verhalten bekannt. In dieser Arbeit werden die drei Methoden „Cone-Splitting”, „Polyhedral Annexation” und „Outer Approximation” zur Steigerung ihrer Effizienz beträchtlich modifiziert. Weiters wird über Implementierung sowie Test und Vergleich an mehr als 100 Beispielen mit bis zu 50 Variablen und 30 Nebenbedingungen (plus Nichtnegativitätsbedingung) berichtet.
    Notes: Abstract Several (theoretical) methods have been proposed for solving concave minimization problems; very little has been done on numerical issues. In this paper, three promising approaches (Cone-Splitting, Polyhedral Annexation and Outer Approximation) are considerably modified in order to enhance efficiency. Furthermore, a report is given on implementation, test and comparison on more than 100 examples with up to 50 variables and 30 linear constraints (plus nonnegativity conditions).
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    A note on the stability of rational Runge-Kutta methods (1989)
    Springer
    Computing 42 (1989), S. 329-339 
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    ISSN: 1436-5057
    Keywords: 65L05 ; 65L20 ; Stability ; rational Runge-Kutta methods ; numerical solution ; stiff ordinary differential equations ; A 0-boundedness ; A 0-contractivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Arbeit befaßt sich mit der Stabilität von rationalen Runge-Kutta-Verfahren bei der numerischen Lösung steifer Anfangswertprobleme. Es wird eine natürliche Stabilitätsforderung, dieA 0-Beschränktheit, formuliert und dann gezeigt, daß es keine rationalen Runge-Kutta-Verfahren gibt, dieA 0-kontraktiv oderA 0-beschränkt sind.
    Notes: Abstract The present paper deals with the stability of rational Runge-Kutta methods in the numerical solution of stiff initial value problems. A natural stability requirement, calledA 0-boundedness, is formulated. It is proved that there exist no rational Runge-Kutta methods which are eitherA 0-contractive orA 0-bounded.
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    Dual and selfdual networks of queues with rejection blocking (1989)
    Springer
    Computing 43 (1989), S. 1-11 
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    ISSN: 1436-5057
    Keywords: Performance Evaluation ; Queueing Networks ; Rejection Blocking ; Equilibrium State Probabilities ; Performance Measures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Offene und geschlossene Warteschlangennetze mit Rückweisungsblockierung und beliebiger Topologie werden untersucht. Durch Verwendung des sogenannten “Lochkonzeptes” wird eine Dualität für Netzwerkpaare entwickelt. Die Dualität bewirkt, daß die Gleichgewichtszustandswahrscheinlichkeiten und Durchsätze des gegebenen und des zugeordneten dualen Netzes gleich sind. Für gewisse geschlossene Netzwerke von Warteschlangen mit Rückweisungsblockierung wird eine exakte Produktformlösung abgeleitet. In diesem Fall ermöglicht die Dualität, Leistungsgrößen mit einfachen Methoden zu bestimmen. In einigen Fällen haben das gegebene und das zu ihm duale Netzwerk die gleiche Struktur. Netzwerke dieser Art werden als selbst-dual bezeichnet. Selbstdualität liefert exakte Beziehungen zwischen Leistungsgrößen von verschiedenen Stationen.
    Notes: Abstract Open and closed queueing networks with rejection blocking are investigated. Using the concept of holes, a duality is derived for pairs of networks. This duality equates equilibrium state probabilities and throughputs of the given network and its dual. As an application an exact product form solution for certain closed queueing networks with rejection blocking are derived. In this case, duality provides a simple method to compute performance measures. In some cases, a network and its dual have the same structure. Duality provides relations among performance measures of different stations in this case.
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    A continuation procedure based on projected Newton steps (1989)
    Springer
    Computing 43 (1989), S. 13-25 
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    ISSN: 1436-5057
    Keywords: 65J15 ; 65R20 ; Fixed point problems ; continuation method ; Newton's method ; nonlinear integral equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Fortsetzungstechnik zur Lösung nichtlinearer Fixpunktprobleme in Hilberträumen vorgestellt und diskutiert. Sie benutzt projezierte Newton-Schritte zur Lösung der Teilprobleme. Numerische Beispiele illustrieren das Verhalten des Verfahrens.
    Notes: Abstract In this paper we present and discuss a continuation method for solving certain fixed point problems in Hilbert spaces. The procedure allows to reduce progressively the residual until a desired level is reached. It is constructed combining a projected variant of Newton's method recently proposed and studied in [6] with the so-called principle of sufficiently weak increase of H. Schwetlick [9], [10]. Numerical examples illustrate the performance of the algorithm.
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    A Farkas-type theorem for linear interval equations (1989)
    Springer
    Computing 43 (1989), S. 93-95 
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    ISSN: 1436-5057
    Keywords: 15A06 ; 15A39 ; 65G10 ; linear interval equations ; nonnegative solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Notwendige und hinreichende Bedingungen für die Existenz einer nichtnegativen Lösung eines linearen Intervallgleichungssystems werden angegeben.
    Notes: Abstract We give a Farkas-type necessary and sufficient condition for a system of linear interval equations to have a nonnegative solution, and derive a consequence of it.
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    Global convergence of Rosen's gradient projection method (1989)
    Springer
    Mathematical programming 44 (1989), S. 357-366 
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    ISSN: 1436-4646
    Keywords: Gradient projection ; algorithm ; global convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The convergence of Rosen's gradient method is a long-standing problem in nonlinear programming. Recently, progress has been made by several researchers. In this paper, we completely resolve the problem.
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    URL: http://dx.doi.org/10.1007/BF01587098
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    The boolean quadric polytope: Some characteristics, facets and relatives (1989)
    Springer
    Mathematical programming 45 (1989), S. 139-172 
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    ISSN: 1436-4646
    Keywords: Unconstrained zero–one quadratic programming ; polyhedral combinatorics ; facets ; polytopes ; vertex-packing ; series-parallel graphs ; polynomial solvability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We study unconstrained quadratic zero–one programming problems havingn variables from a polyhedral point of view by considering the Boolean quadric polytope QP n inn(n+1)/2 dimensions that results from the linearization of the quadratic form. We show that QP n has a diameter of one, descriptively identify three families of facets of QP n and show that QP n is symmetric in the sense that all facets of QP n can be obtained from those that contain the origin by way of a mapping. The naive linear programming relaxation QP n LP of QP n is shown to possess the Trubin-property and its extreme points are shown to be {0,1/2,1}-valued. Furthermore, O(n 3) facet-defining inequalities of QP n suffice to cut off all fractional vertices of QP n LP, whereas the family of facets described by us has at least O(3 n ) members. The problem is also studied for sparse quadratic forms (i.e. when several or many coefficients are zero) and conditions are given for the previous results to carry over to this case. Polynomially solvable problem instances are discussed and it is shown that the known polynomiality result for the maximization of nonnegative quadratic forms can be obtained by simply rounding the solution to the linear programming relaxation. In the case that the graph induced by the nonzero coefficients of the quadratic form is series-parallel, a complete linear description of the associated Boolean quadric polytope is given. The relationship of the Boolean quadric polytope associated to sparse quadratic forms with the vertex-packing polytope is discussed as well.
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    Odd cycles and matrices with integrality properties (1989)
    Springer
    Mathematical programming 45 (1989), S. 279-294 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A cycle of a bipartite graphG(V+, V−; E) is odd if its length is 2 (mod 4), even otherwise. An odd cycleC is node minimal if there is no odd cycleC′ of cardinality less than that ofC′ such that one of the following holds:C′ ∩V + ⊂C ∩V + orC′ ∩V − ⊂C ∩V −. In this paper we prove the following theorem for bipartite graphs: For a bipartite graphG, one of the following alternatives holds: -All the cycles ofG are even. -G has an odd chordless cycle. -For every node minimal odd cycleC, there exist four nodes inC inducing a cycle of length four. -An edge (u, v) ofG has the property that the removal ofu, v and their adjacent nodes disconnects the graphG. To every (0, 1) matrixA we can associate a bipartite graphG(V+, V−; E), whereV + andV − represent respectively the row set and the column set ofA and an edge (i,j) belongs toE if and only ifa ij = 1. The above theorem, applied to the graphG(V+, V−; E) can be used to show several properties of some classes of balanced and perfect matrices. In particular it implies a decomposition theorem for balanced matrices containing a node minimal odd cycleC, having the property that no four nodes ofC induce a cycle of length 4. The above theorem also yields a proof of the validity of the Strong Perfect Graph Conjecture for graphs that do not containK 4−e as an induced subgraph.
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    Parallel coding of binary images (1989)
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    Computing 41 (1989), S. 1-17 
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    ISSN: 1436-5057
    Keywords: 68C05 ; Coding of binary images ; data compression ; parallel algorithms ; erosion ; dilation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In der Bildverarbeitung sind aufgrund der zu manipulierenden großen Datenmengen effiziente Codierungsmethoden zur Datenkompression sowohl bei der Ausführung von Algorithmen als auch bei der Übertragung und Speicherung von Bilddaten erforderlich. Während für sequentielle Rechner zahlreiche Codierungsverfahren entwickelt wurden, werden Codierungsmethoden für parallele Rechner weniger untersucht. In der vorliegenden Arbeit werden vorwiegend auf Heuristik basierende parallele Algorithmen zur Codierung von Binärbildern entwickelt. Dabei stehen im Vordergrund die Datenkompression von Binärbildern zur Archivierung oder Übertragung von Bilddaten einerseits und die Beschreibung deren zugrundeliegender stochastischer Szenen (aus der Materialkunde, Biologie ...) im Sinne einer Klassifikation nach Größe und Form der Bildkomponenten andererseits.
    Notes: Abstract Due to the large amount of data to be manipulated in image processing, efficient coding methods for data compression are necessary both for the execution of algorithms, and for transmission and storage of pictorial data. While for sequential computers many coding methods have been developed, they have been less investigated so far for parallel computers. In the present work parallel coding algorithms, mainly based upon heuristics, are developed. Great importance is attributed to data compression of binary images for filing or transmission on the one hand, and to description of the underlying stochastic scenes (from material science, biology ...), in terms of a classification by size and shape of the components of the image on the other hand.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238726
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  • 98
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    An interval method for bounding level sets of parameter estimation problems (1989)
    Springer
    Computing 41 (1989), S. 75-86 
    Details
    ISSN: 1436-5057
    Keywords: 65K05 ; 90C30 ; Parameter estimation ; level set ; inclusion function ; interval arithmetic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine neue Methode vorgestellt für die Beschränkung der Niveaumengen von nichtlinearen Parameterschätzungsaufgaben mit Zielfunktion von Quadratsummen-Form unter Verwendung von Inklusionsfunktionen und Intervallarithmetik. Die Ergebnismenge, die eine Niveaumenge beschränkt, bietet mehr Informationen für den Benutzer als die üblichen lokalen Minimum-Punkte. Die Konvergenzgeschwindigkeit ist im allgemeinen linear, in Spezialfällen kann sie superlinear oder höher sein. Die Konvergenzbedingungen werden untersucht und Beispiele gezeigt.
    Notes: Abstract A new method is presented using inclusive functions and interval arithmetic for bounding the level sets of nonlinear parameter estimation problems with objective function of sum-of-squares type. The result box bounding a level set conveys more information for the user than the usual local minimum points do. The rate of convergence is in general linear, in special cases it can be superlinear or higher. The condition of convergence is studied, and examples are shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238730
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  • 99
    Electronic Resource
    Electronic Resource
    A uniform numerical method for quasilinear singular perturbation problems without turning points (1989)
    Springer
    Computing 41 (1989), S. 97-106 
    Details
    ISSN: 1436-5057
    Keywords: 65L10 ; 65L50 ; Singular perturbations ; boundary value problems ; finite differences ; uniform stability ; consistency and convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ein numerisches Verfahren für quasilineare, singulär gestörte Randwertaufgaben ohne Umkehrpunkte wird angegeben: das kontinuierliche Problem wird durch spezielle neue unabhängige Variable transformiert und danach werden Differenzenverfahren verwendet. Die Konvergenz erster Ordnung gleichmäßig bezüglich des Störungsparameters wird in der diskretenL 1-Norm bewiesen. Die numerischen Ergebnisse zeigen auch punktweise Konvergenz.
    Notes: Abstract A numerical method for singularly perturbed quasilinear boundary value problems without turning points is proposed: the continuous problem is transformed by introducing a special new independent variable and then finite-difference schemes are applied. The first order convergence uniform in the perturbation parameter is proved in the discreteL 1-norm. The numerical results show the pointwise convergence, too.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238732
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  • 100
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    Electronic Resource
    Error estimates for discretized differential inclusions (1989)
    Springer
    Computing 41 (1989), S. 349-358 
    Details
    ISSN: 1436-5057
    Keywords: 34A60 ; 49D25 ; 65L05 ; Differential inclusions ; discrete approximations ; Euler scheme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Eine Abschätzung der Hausdorff-Distanz zwischen der Menge aller Lösungen einer Differentialeinschließung und der Eulerschen Approximation dieser Einschließung wird vorgelegt, wobei ein Stetigkeitsmodul für Multifunktionen angewendet wird. Eine numerische Prozedur zur Auffindung einer gewissen Lösung der diskretisierten Einschließung wird vorgeschlagen.
    Notes: Abstract We present an estimate for the Hausdorff distance between the set of solutions of a differential inclusion and the set of solutions of its Euler discrete approximation, using an averaged modulus of continuity for multifunctions. A computational procedure to obtain a certain solution of the discretized inclusion is proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241223
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