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  • Articles  (674)
  • Springer  (674)
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  • 1985-1989  (674)
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  • 1985  (674)
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  • Articles  (674)
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  • 1985-1989  (674)
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  • 1
    Electronic Resource
    Electronic Resource
    Sequential location-allocation problems on chains and trees with probabilistic link demands (1985)
    Springer
    Mathematical programming 32 (1985), S. 249-277 
    Details
    ISSN: 1436-4646
    Keywords: Minisum Locations ; Location-Allocation ; Network Location ; Dynamic Location
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we consider multiperiod minisum location problems on networks in which demands can occur continuously on links according to a uniform probability density function. In addition, demands may change dynamically over time periods and at most one facility can be located per time period. Two types of networks are considered in conjunction with three behavioral strategies. The first type of network discussed is a chain graph. A myopic strategy and long-range strategy for locatingp-facilities are considered, as is a discounted present worth strategy for locating two facilities. Although these problems are generally nonconvex, effective methods are developed to readily identify all local and global minima. This analysis forms the basis for similar problems on tree graphs. In particular, we construct algorithms for the 3-facility myopic problem and the 2-facility long-range and discounted cost problems on a tree graph. Extensions and suggestions for further research on problems involving more general networks are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582049
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  • 2
    Electronic Resource
    Electronic Resource
    On market prices in linear production games (1985)
    Springer
    Mathematical programming 32 (1985), S. 366-370 
    Details
    ISSN: 1436-4646
    Keywords: Cores ; Dual Prices ; Linear Production Games
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consider a game in which resources may be combined to produce products of known values. For linear production processes, the game may be characterized by a family of linear programs. It is shown that appropriately defined market prices for the resources coincide with the set of optimal dual solutions to one of these linear programs. This result generalizes and unifies the known cases in game theory, in which the core of a game coincides with the set of dual optimal solutions to a corresponding master linear programming problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582055
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  • 3
    Electronic Resource
    Electronic Resource
    Globally convergent conjugate gradient algorithms (1985)
    Springer
    Mathematical programming 33 (1985), S. 61-67 
    Details
    ISSN: 1436-4646
    Keywords: Conjugate Gradient Methods ; Global Convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The paper examines a method of implementing an angle test for determining when to restart conjugate gradient methods in a steepest descent direction. The test is based on guaranteeing that the cosine of the angle between the search direction and the negative gradient is within a constant multiple of the cosine of the angle between the Fletcher-Reeves search direction and the negative gradient. This guarantees convergence, for the Fletcher-Reeves method is known to converge. Numerical results indicate little, if anything, is lost in efficiency, and indicate gains may well be possible for large problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582011
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  • 4
    Electronic Resource
    Electronic Resource
    Working conference on computational issues in combinatorial optimization (1985)
    Springer
    Mathematical programming 33 (1985), S. 120-121 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582016
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  • 5
    Electronic Resource
    Electronic Resource
    Performance evaluation of nonlinear optimization methods via pairwise comparison and fuzzy numbers (1985)
    Springer
    Mathematical programming 33 (1985), S. 93-114 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Optimization ; Pairwise Comparison ; Priority Theory ; Fuzzy Sets ; Triangular Membership Functions ; Performance Evaluation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we extend the deterministic performance evaluation of nonlinear optimization methods: we carry out a pairwise comparison using fuzzy estimates of the performance ratios to obtain fuzzy final scores of the methods under consideration. The key instrument is the concept of fuzzy numbers with triangular membership functions. The algebraic operations on them are simple extensions of the operations on real numbers; they are exact in the parameters (lower, modal, and upper values), not necessarily exact in the shape of the membership function. We illustrate the fuzzy performance evaluation by the ranking and rating of five methods (geometric programming and four general methods) for solving geometric-programming problems, using the results of recent computational studies. Some general methods appear to be leading, an outcome which is not only due to their performance under subjective criteria like domain of applications and conceptual simplicity of use; they also score higher under more objective criteria like robustness and efficiency.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582014
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  • 6
    Electronic Resource
    Electronic Resource
    On the complexity of four polyhedral set containment problems (1985)
    Springer
    Mathematical programming 33 (1985), S. 139-145 
    Details
    ISSN: 1436-4646
    Keywords: Computational Complexity ; NP-Complete ; Linear Program ; Polyhedron ; Cell
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A nonempty closed convex polyhedronX can be represented either asX = {x: Ax ⩽b}, where (A, b) are given, in which caseX is called anH-cell, or in the formX = {x: x = Uλ + Vμ, Σλ j = 1,λ ⩾ 0,μ ⩾ 0}, where (U, V) are given, in which caseX is called aW-cell. This note discusses the computational complexity of certain set containment problems. The problems of determining if $$X \nsubseteq Y$$ , where (i)X is anH-cell andY is a closed solid ball, (ii)X is anH-cell andY is aW-cell, or (iii)X is a closed solid ball andY is aW-cell, are all shown to be NP-complete, essentially verifying a conjecture of Eaves and Freund. Furthermore, the problem of determining whether there exists an integer point in aW-cell is shown to be NP-complete, demonstrating that regardless of the representation ofX as anH-cell orW-cell, this integer containment problem is NP-complete.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582241
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  • 7
    Electronic Resource
    Electronic Resource
    Simplex pivots on the set packing polytope (1985)
    Springer
    Mathematical programming 33 (1985), S. 123-138 
    Details
    ISSN: 1436-4646
    Keywords: Set Packing ; Integer Programming ; Linear Programming ; Simplex Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper considers the set packing problem max{wx: Ax ⩽ b, x ⩾ 0 and integral}, whereA is anm × n 0–1 matrix,w is a 1 ×n weight vector of real numbers andb is anm × 1 vector of ones. In equality form, its linear programming relaxation is max{wx: (x, y) ∈P(A)} whereP(A) = {(x, y):Ax +I m y =b, x⩾0,y⩾0}. Letx 1 be any feasible solution to the set packing problem that is not optimal and lety 1 =b − Ax 1; then (x 1,y 1) is an integral extreme point ofP(A). We show that there exists a sequence of simplex pivots from (x 1,y 1) to (x*,y*), wherex* is an optimal solution to the set packing problem andy* =b − Ax*, that satisfies the following properties. Each pivot column has positive reduced weight and each pivot element equals plus one. The number of pivots equals the number of components ofx* that are nonbasic in (x 1,y 1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582240
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  • 8
    Electronic Resource
    Electronic Resource
    The traveling salesman problem on a graph and some related integer polyhedra (1985)
    Springer
    Mathematical programming 33 (1985), S. 1-27 
    Details
    ISSN: 1436-4646
    Keywords: Traveling Salesman Problem ; Integer Polyhedron ; Facet ; Graph ; Series-Parallel Graph ; Steiner Tree ; Polynomial Algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Given a graphG = (N, E) and a length functionl: E → ℝ, the Graphical Traveling Salesman Problem is that of finding a minimum length cycle goingat least once through each node ofG. This formulation has advantages over the traditional formulation where each node must be visited exactly once. We give some facet inducing inequalities of the convex hull of the solutions to that problem. In particular, the so-called comb inequalities of Grötschel and Padberg are generalized. Some related integer polyhedra are also investigated. Finally, an efficient algorithm is given whenG is a series-parallel graph.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582008
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  • 9
    Electronic Resource
    Electronic Resource
    On constraint sets of infinite linear programs over ordered fields (1985)
    Springer
    Mathematical programming 33 (1985), S. 146-161 
    Details
    ISSN: 1436-4646
    Keywords: Infinite Linear Programming ; Ordered Fields ; Extreme Points ; Extreme Directions ; Opposite Sign Property ; Nonlinear Equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper provides a characterization of extreme points and extreme directions of the subsets of the space of generalized finite sequences occurring as the constraint sets of semi-infinite or infinite linear programs. The main result is that these sets are generated by (possibly infinitely many) extreme points and extreme directions. All results are valid over arbitrary ordered fields.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582242
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  • 10
    Electronic Resource
    Electronic Resource
    A simplex algorithm for piecewise-linear programming I: Derivation and proof (1985)
    Springer
    Mathematical programming 33 (1985), S. 204-233 
    Details
    ISSN: 1436-4646
    Keywords: Linear Programming ; Simplex Methods ; Piecewise-Linear Programming ; Nondifferentiable Optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise-linear objective, subject to linear constraints. This three-part paper develops and analyzes a general, computationally practical simplex algorithm for piecewiselinear programming. Part I derives and justifies the essential steps of the algorithm, by extension from the simplex method for linear programming in bounded variables. The proof employs familiar finite-termination arguments and established piecewise-linear duality theory. Part II considers the relaxation of technical assumptions pertaining to finiteness, feasibility and nondegeneracy of piecewise-linear programs. Degeneracy is found to have broader consequences than in the linear case, and the standard techniques for prevention of cycling are extended accordingly. Part III analyzes the computational requirements of piecewise-linear programming. The direct approach embodied in the piecewise-linear simplex algorithm is shown to be inherently more efficient than indirect approaches that rely on transformation of piecewise-linear programs to equivalent linear programs. A concluding section surveys the many applications of piecewise-linear programming in linear programming,l 1 estimation, goal programming, interval programming, and nonlinear optimization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582246
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  • 11
    Electronic Resource
    Electronic Resource
    A new algorithm for solving variational inequalities with application to the traffic assignment problem (1985)
    Springer
    Mathematical programming 33 (1985), S. 339-351 
    Details
    ISSN: 1436-4646
    Keywords: Variational Inequality ; Nondifferentiable Optimization ; Nonconvex Programming ; Network Optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The variational inequality problem in Euclidian space is formulated as a nonconvex, nondifferentiable optimization problem. We show that any stationary point is optimal, and we propose a solution algorithm that decreases the nondifferential objective monotonically. Application to the asymmetric traffic assignment problem is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584381
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  • 12
    Electronic Resource
    Electronic Resource
    Treatment of engineering design constraints in a relational data base (1985)
    Springer
    Engineering with computers 1 (1985), S. 27-37 
    Details
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01200336
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  • 13
    Electronic Resource
    Electronic Resource
    Simple bounds for solutions of monotone complementarity problems and convex programs (1985)
    Springer
    Mathematical programming 32 (1985), S. 32-40 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Complementarity ; Monotonicity ; Convexity ; Bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For a solvable monotone complementarity problem we show that each feasible point which is not a solution of the problem provides simple numerical bounds for some or all components of all solution vectors. Consequently for a solvable differentiable convex program each primal-dual feasible point which is not optimal provides simple bounds for some or all components of all primal-dual solution vectors. We also give an existence result and simple bounds for solutions of monotone compementarity problems satisfying a new, distributed constraint qualification. This result carries over to a simple existence and boundedness result for differentiable convex programs satisfying a similar constraint qualification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585657
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  • 14
    Electronic Resource
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    On the refinement of bounds of heuristic algorithms for the traveling salesman problem (1985)
    Springer
    Mathematical programming 32 (1985), S. 114-117 
    Details
    ISSN: 1436-4646
    Keywords: Traveling Salesman Problem ; Heuristics ; Approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A number of heuristics for the traveling salesman problem (TSP) rely on the assumption that the triangle inequality (TI) is satisfied. When TI does not hold, the paper proposes a transformation such that for the transformed problem the TI holds. Consequently, the bounds obtained for heuristics are valid with appropriate modification. Moreover, for a TSP satisfying TI the same transformation strengthens such bounds. The transformation essentially maps the problem into one that is minimal with respect to the property that TI holds. For the symmetric TSP the transformation is particularly simple. For an application of the transformation in the asymmetric case we need the dual solution of an assignment problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585662
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  • 15
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    Computing optimal scalings by parametric network algorithms (1985)
    Springer
    Mathematical programming 32 (1985), S. 1-10 
    Details
    ISSN: 1436-4646
    Keywords: Scaling ; Network Algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Asymmetric scaling of a square matrixA ≠ 0 is a matrix of the formXAX −1 whereX is a nonnegative, nonsingular, diagonal matrix having the same dimension ofA. Anasymmetric scaling of a rectangular matrixB ≠ 0 is a matrix of the formXBY −1 whereX andY are nonnegative, nonsingular, diagonal matrices having appropriate dimensions. We consider two objectives in selecting a symmetric scaling of a given matrix. The first is to select a scalingA′ of a given matrixA such that the maximal absolute value of the elements ofA′ is lesser or equal that of any other corresponding scaling ofA. The second is to select a scalingB′ of a given matrixB such that the maximal absolute value of ratios of nonzero elements ofB′ is lesser or equal that of any other corresponding scaling ofB. We also consider the problem of finding an optimal asymmetric scaling under the maximal ratio criterion (the maximal element criterion is, of course, trivial in this case). We show that these problems can be converted to parametric network problems which can be solved by corresponding algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585655
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  • 16
    Electronic Resource
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    Local properties of algorithms for minimizing nonsmooth composite functions (1985)
    Springer
    Mathematical programming 32 (1985), S. 69-89 
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    ISSN: 1436-4646
    Keywords: Composite Functions ; Nonsmooth Optimization ; Structure Functionals ; Superlinear Convergence ; Second Order Convergence ; Strong Uniqueness ; Reduced Curvature ; 90 C 30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper considers local convergence and rate of convergence results for algorithms for minimizing the composite functionF(x)=f(x)+h(c(x)) wheref andc are smooth buth(c) may be nonsmooth. Local convergence at a second order rate is established for the generalized Gauss—Newton method whenh is convex and globally Lipschitz and the minimizer is strongly unique. Local convergence at a second order rate is established for a generalized Newton method when the minimizer satisfies nondegeneracy, strict complementarity and second order sufficiency conditions. Assuming the minimizer satisfies these conditions, necessary and sufficient conditions for a superlinear rate of convergence for curvature approximating methods are established. Necessary and sufficient conditions for a two-step superlinear rate of convergence are also established when only reduced curvature information is available. All these local convergence and rate of convergence results are directly applicable to nonlinearing programming problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585659
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  • 17
    Electronic Resource
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    Solving large-scale mixed-integer programs with fixed charge variables (1985)
    Springer
    Mathematical programming 32 (1985), S. 165-182 
    Details
    ISSN: 1436-4646
    Keywords: Mixed-Inter Programming ; Fixed Charge Problems ; Preprocessing of Mixed-Integer Programs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider large-scale mixed-integer programming problems containing fixed charge variables. In practice such problems are frequently approached by using commercial mathematical programming systems. Depending on the formulation, size and structure of the problem this approach may or may not be successful. We describe algorithms for preprocessing and optimization of such problems and discuss the design of an experimental software system based on MPSX/370. Numerical results for solving some large real life problems are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586089
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  • 18
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    Applications of the method of partial inverses to convex programming: Decomposition (1985)
    Springer
    Mathematical programming 32 (1985), S. 199-223 
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    ISSN: 1436-4646
    Keywords: Monotone Multifunction ; Separable Convex Programming ; Proximal Point Algorithm ; Decomposition Algorithm ; Resource Allocation ; Large-Scale Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A primal–dual decomposition method is presented to solve the separable convex programming problem. Convergence to a solution and Lagrange multiplier vector occurs from an arbitrary starting point. The method is equivalent to the proximal point algorithm applied to a certain maximal monotone multifunction. In the nonseparable case, it specializes to a known method, the proximal method of multipliers. Conditions are provided which guarantee linear convergence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586091
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  • 19
    Electronic Resource
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    On uniqueness of Kuhn-Tucker multipliers in nonlinear programming (1985)
    Springer
    Mathematical programming 32 (1985), S. 242-246 
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    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Kuhn—Tucker Multipliers ; Constraint Qualifications ; Second Order Conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Recently Fujiwara, Han and Mangasarian introduced a new constraint qualification which is a slight tightening of the well-known Mangasarian—Fromovitz constraint qualification. We show that this new qualification is a necessary and sufficient condition for the uniqueness of Kuhn—Tucker multipliers. We also show that it implies the satisfaction of second order necessary optimality conditions at a local minimum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586095
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  • 20
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    Parallel variable metric algorithms for unconstrained optimization (1985)
    Springer
    Mathematical programming 33 (1985), S. 68-81 
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    ISSN: 1436-4646
    Keywords: Unconstrained Optimization ; Parallel Computers ; Parallel Processing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We classify Straeter's ideas for parallel unconstrained optimization and apply them to Huang's class of updating formulas. Straeter's rank-one updating formula appears to be the only parallel extension within Huang's class with the property of quadratic termination. We also develop a parallel extension of Broyden's (1965) rank-one updating formula and prove quadratic termination. Finally, we present numerical results, obtained by testing the algorithms on several standard example problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582012
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  • 21
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    Multivariate rational interpolation (1985)
    Springer
    Computing 34 (1985), S. 41-61 
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    ISSN: 1436-5057
    Keywords: 41A05 ; 41A20 ; 41A63 ; Multivariate functions ; rational interpolation ; branched continued fractions ; multivariate Padé approximants ; recursive calculation of interpolants ; multivariate inverse differences
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das multivariate polynomiale Interpolationsproblem sowie die multivariate Padé-Approximation sind schon einige Jahre alt, aber das multivariate rationale Interpolationsproblem ist noch verhältnismäßig jung [3,8]. Für univariate Funktionen gibt es verschiedene äquivalente Algorithmen zur Berechnung vom rationalen Interpolant: die Lösung eines Gleichungssystems, die rekursive Berechnung oder die Berechnung eines Kettenbruchs. Diese Algorithmen werden hier verallgemeinert auf multivariate Funktionen. Wir bemerken, daß sie nun nicht mehr equivalent sind. Diese Beobachtung ist auch schon von anderen Mathematikern gemacht worden für das multivariate Padé-Approximationsproblem [2,7], das man auch auf verschiedene Weisen lösen kann.
    Notes: Abstract Many papers have already been published on the subject of multivariate polynomial interpolation and also on the subject of multivariate Padé approximation. But the problem of multivariate rational interpolation has only very recently been considered; we refer among others to [8] and [3]. The computation of a univariate rational interpolant can be done in various equivalent ways: one can calculate the explicit solution of the system of interpolatory conditions, or start a recursive algorithm, or calculate the convergent of a continued fraction. In this paper we will generalize each of those methods from the univariate to the multivariate case. Although the generalization is simple, the equivalence of the computational methods is completely lost in the multivariate case. This was to be expected since various authors have already remarked [2,7] that there is no link between multivariate Padé approximants calculated by matching the Taylor series and those obtained as convergents of a continued fraction.
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    URL: http://dx.doi.org/10.1007/BF02242172
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  • 22
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    On solving nonlinear least-squares problems in case of rankdeficient Jacobians (1985)
    Springer
    Computing 34 (1985), S. 63-72 
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    ISSN: 1436-5057
    Keywords: Primary: 65H10, 65K05 ; Secondary: 65F20 ; Nonlinear least-squares problems ; rankdeficient Jacobians ; Gauss-Newton method ; local convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Gegenstand der Arbeit ist die Lösung nichtlinearer Quadratmittelproblemeg(x):=1/2F(x) T F(x)→Min!,F:ℝ n ℝ m ,m≧n, für die die Jacobi-MatrixF′(x*) in einem Lösungspunktx * rangdefizient ist. Es wird ein HilfsquadratmittelproblemG(u)→Min!,u≔(x,d) T, höherer Dimension konstruiert, von dem Gutartigkeit gezeigt werden kann, falls die Rangdefizienzr vonF′(x*) klein ist. Überdies wird bewiesen, daß für beliebigesr im konsistenten Fallg(x*)=0 die Gauss-Newton-Folge {x k} mindestensQ-linear gegenx * konvergiert.
    Notes: Abstract This paper is concerned with solving nonlinear least-squares problemsg(x):=1/2F(x) T F(x)→Min!,F:ℝ n ℝ m ,m≧n having at a solution pointx * the rankdeficient JacobianF′(x*). An auxiliary least-squares problemG(u)→Min!,u≔(x, d) T of higher dimension is constructed which can be shown to be a well-posed one if the rank deficiencyr ofF′(x*) is small. Moreover, it is proved that for arbitraryr in the consistent caseg(x*)=0 the Gauss-Newton sequence {x k} converges at leastQ-linearly tox *.
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    URL: http://dx.doi.org/10.1007/BF02242173
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  • 23
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    Varying relaxation parameters in nonlinear successive overrelaxation (1985)
    Springer
    Computing 34 (1985), S. 81-85 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir verallgemeinern das “free steering theorem” im Ostrowski, das hinreichende Konvergenzbedingungen für lineare SOR-Verfahren mit variablen Relaxationsparametern angibt, auf nichtlineare Probleme.
    Notes: Abstract We derive here a generalization to nonlinear problems of the “free steering theorem” of Ostrowski on sufficient conditions for convergence of linear SOR with varying relaxation parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02242175
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  • 24
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    A bounding approach to calculating α1/p (1985)
    Springer
    Computing 34 (1985), S. 87-89 
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    ISSN: 1436-5057
    Keywords: 65D15 ; 65G10 ; p-th roots ; interval arithmetic estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine einfache Methode angegeben, die quadratische von oben und von unter gegen α1/p strebende Folgen erzeugt.
    Notes: Abstract A simple method is exhibited for obtaining sequences which tend quadratically to α1/p from above and below.
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    URL: http://dx.doi.org/10.1007/BF02242176
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  • 25
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    Asynchronous algorithms for poisson's equation with nonlinear boundary conditions (1985)
    Springer
    Computing 34 (1985), S. 155-168 
    Details
    ISSN: 1436-5057
    Keywords: 65 H 10 ; 65 M 20 ; CR: 5.15 ; 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Poisson-Gleichung mit nichtlinearen Randbedingungen wird mittels der Linienmethode diskretisiert und ergibt ein System von gewöhnlichen Differentialgleichungen zweiter Ordnung mit Randbedingungen. Durch invariante Einbettung für jedes eindimensionale Problem wird dieses System in ein Fixpunktproblem verwandelt, auf das dann die asynchronen Algorithmen angewandt werden.
    Notes: Abstract Poisson's equation with nonlinear boundary conditions is discretized with the method of lines to obtain a system of second order differential equations with multi-point boundary conditions. This differential system is converted, using invariant imbedding for each one-dimensional problem, into a fixed point problem and then the asynchronous algorithms are applied.
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    A new method for automatical computation of error bounds for the set of all solutions of nonlinear boundary value problems (1985)
    Springer
    Computing 34 (1985), S. 131-154 
    Details
    ISSN: 1436-5057
    Keywords: 65N 15 ; 34 B 15 ; Algorithm for a priori bounds ; boundary value problems with arbitrary many solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden nichtlineare gewöhnliche Randwertaufgaben zweiter Ordnung mit beliebig vielen LösungenuεC 2[a, b] behandelt. In dieser Arbeit wird ein Algorithmus zur Berechnung von a priori Schranken $$\bar u,\bar d \in C[a,b]$$ eingeführt. Für die Schranken $$\bar u$$ und % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmizayaara% aaaa!36EE!\[\bar d\] werden die folgenden Eigenschaften garantiert. 1. Für jede Lösungu des behandelten nichtlinearen Problems gelten $$\bar u(x) \leqslant u(x) \leqslant \bar u(x), - \bar d(x) \leqslant u'(x) \leqslant \bar d(x)$$ für jedesxε[a, b]. 2. Die Schranken $$\bar u$$ und % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmizayaara% aaaa!36EE!\[\bar d\] werden mit Hilfe der Funktionen exp, sin und cos definiert. 3. Die Schranken $$\bar u$$ und % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmizayaara% aaaa!36EE!\[\bar d\] werden ohne Kenntnis von Lösungen und der Zahl der Lösungen berechnet.
    Notes: Abstract We consider nonlinear boundary value problems with arbitrarily many solutionsuεC 2 [a, b]. In this paper an Algorithm will be established for a priori bounds $$\bar u,\bar d \in C[a,b]$$ with the following properties: 1. For every solutionu of the nonlinear problem we obtain $$\bar u(x) \leqslant u(x) \leqslant \bar u(x), - \bar d(x) \leqslant u'(x) \leqslant \bar d(x)$$ for any,xε[a, b]. 2. The bounds $$\bar u$$ and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmizayaara% aaaa!36EE!\[\bar d\] are defined by the use of the functions exp, sin and cos. 3. We use neither the knowledge of solutions nor the number of solutions.
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    Minimal quadrature formulae for the spaces H 2 R and L 2 R . A unified interpolatory approach (1985)
    Springer
    Computing 34 (1985), S. 169-177 
    Details
    ISSN: 1436-5057
    Keywords: 65 D 30 ; Numerical integration ; minimal formulae
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Minimale Quadraturformeln für die HilberträumeH 2 R undL 2 R werden untersucht. Diese Räume enthalten die Funktionen, die analytisch sind in der offenen Kreisscheibe mit RadiusR und Zentrum im Ursprung der komplexen Ebene; die Skalarprodukte sind als Rand- bzw. Flächenintegrale definiert. Solche Formeln kann man interpolatorisch interpretieren, indem man den Markoffschen Zugang zu Gaußschen Formeln in zweierlei Hinsicht verallgemeinert. Dies geschieht für beide Räume simultan, man benutzt denselben Interpolationsoperator. Dieser Zugang bietet den Vorteil, daß man ein System nichtlinearer Gleichungen allein für die Stützstellen minimaler Formeln erhält, im Gegensatz zu dem gekoppelten System für Stützstellen und Gewichte, das sich aus den Minimalitätsbedingungen ergibt. Das entkoppelte System kann numerisch gelöst werden, die entstehenden Formeln sind sehr gut geeignet zur Integration von Funktionen mit Randsingularitäten.
    Notes: Abstract We consider minimal quadrature formulae for the Hilbert spacesH 2 R andL 2 R consisting of functions which are analytical on the open disc with radiusR and centre at the origin; the inner products are the boundary contour integral forH 2 R and the area integral over the disc forL 2 R . Such formulae can be viewed as interpolatory, generalizing—in two ways—Markoff's idea to construct the classical Gaussian quadratur formulae. This can be done simultaneously for both spaces using the same Hermitian interpolating operator. The advantage of this approach to minimal formulae is that we get a nonlinear system of equations for the nodes of the minimal formulae alone, in contrast to the coupled system for nodes and weights which arises from the minimality conditions. The uncoupled system that we obtain is numerically solvable for reasonable numbers of nodes and numerical tests show that the resulting minimal formulae are very well suited for the integration of functions with boundary singularities.
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    Local error estimation by doubling (1985)
    Springer
    Computing 34 (1985), S. 179-190 
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    ISSN: 1436-5057
    Keywords: 65 L 05 ; Doubling ; Richardson extrapolation ; error estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Schrittverdopplung, oder Richardson-Extrapolation, ist ein allgemeines Prinzip zur Schätzung des lokalen Fehlers eines Einschrittverfahrens zur numerischen Lösung eines Anfangswertproblems für Systeme gewöhnlicher Differentialgleichungen. Es werden einige Beiträge zur Theorie dieses Vorgehens gemacht. Die Prinzipien zum Vergleich expliziter Runge-Kutta-Formeln werden betrachtet und durch eine ausgewogene Bewertung des Verdoppelns bei Formeln vierter Ordnung illustriert. Einige scheinbar widersprüchliche Vergleiche aus der Literatur werden aufgeklärt.
    Notes: Abstract Doubling, or Richardson extrapolation, is a general principle for the estimation of the local error made by a one-step method for the numerical solution of the initial value problem for a system of ordinary differential equations. Some contributions are made to the theory of doubling. Principles of comparing explicit Runge-Kutta formulas are reviewed and illustrated in a balanced appraisal of doubling in the context of fourth order formulas. Some apparently contradictory comparisons in the literature are explained.
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    URL: http://dx.doi.org/10.1007/BF02259844
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    A low complexity explicit rational centered form (1985)
    Springer
    Computing 34 (1985), S. 261-263 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Eine zentrische Form kleiner Komplexität für rationale Funktionen wird definiert. Einige numerische Beispiele werden angegeben.
    Notes: Abstract A centered form of very low complexity is defined for rational functions. Some numerical examples are calculated.
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    Arithmetically improved algorithmic performance (1985)
    Springer
    Computing 35 (1985), S. 153-175 
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    ISSN: 1436-5057
    Keywords: 65B99 ; Algorithmic performance ; accelerating algorithms ; accelerating convergence ; fully accurate inner product
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ein erweiterter Satz in Gleitkomma-Operationen, der das genaue innere Produkt enthält, bürgt bei der routinemäßigen Verwendung in einigen klassischen iterativen numerischen Algorithmen Vorteile. Diese bestehen darin, daß zur Erreichung von algorithmischen Konvergenzkriterien weniger Iterationen notwendig sind bzw. für eine vorgegebene Anzahl von Iterationen eine höhere Genauigkeit erreicht wird. Nicht alle Algorithmen werden verbessert; günstige Ergebnisse wurden für den QR-Algorithmus, für den CG-Algorithmus und für die Bestimmung einer trennenden Hyperebene erzielt.
    Notes: Abstract An augmented set of floating-point arithmetic operations which includes the accurate inner product can be routinely employed with benefit in some standard iterative numerical algorithms. Benefits include the requirement of fewer iterations for achieving computational convergence criteria and more accurate results for a given number of iterations. Not all algorithms are benefited, but favorable results have been obtained for the QR algorithm, the conjugate gradient algorithm and the separating hyperplane algorithm.
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    Über ein Iterationsverfahren zur Einschließung der inversen Matrix (1985)
    Springer
    Computing 35 (1985), S. 185-188 
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    ISSN: 1436-5057
    Keywords: 65G10 ; 65F30 ; Interval methods ; iteration methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract We consider a modified method of [1] for the improvement of an inclusion of the inverse of a matrix. It is shown that this modification is more efficient than the original method.
    Notes: Zusammenfassung Wir betrachten eine Modifikation eines Verfahrens aus [1] zur iterativen Verbesserung der Einschließung für die Inverse einer Matrix. Für diese Modifikation läßt sich zeigen, daß sie effizienter ist als das ursprüngliche Verfahren.
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    On higher order centered forms (1985)
    Springer
    Computing 35 (1985), S. 177-184 
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    ISSN: 1436-5057
    Keywords: 65G10 ; Interval arithmetic ; range of values
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für den Fall, daßf eine Darstellung der Formf(x)=f(c)+(x-c) n h(x), xεX, besitzt, geben wir eine intervallmäßige Auswertung an, die den Wertebereich über dem kompakten IntervalX mit der Ordnungn+1 approximiert. Fürn=1 erhält man die bekannten Aussagen über die zentrierte Form.
    Notes: Abstract If the real-valued mappingf has a representation of the formf(x)=f(c)+(x-c) n h(x), xεX, then we introduce an interval expression which approximates the range of values off over the compact intervalX with ordern+1. The well known centered form is the special casen=1 of this result.
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    Including iterations for the lambda-matrix eigenproblem (1985)
    Springer
    Computing 35 (1985), S. 207-218 
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    ISSN: 1436-5057
    Keywords: 65H ; Including iterations ; eigenproblem ; interval analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird eine allgemeine systematische Methode für die Berechnung von Nullstellen nichtlinearer Polynomgleichungen diskutiert. Das allgemeine Eigenwertproblem ist ein besonderer Schwerpunkt. Die Methode basiert auf der expliziten. Darstellung des Steigerungsoperators. Diese Darstellung ist auf die Aufspaltung von polynomen in mehrere Variablen begründet.
    Notes: Abstract We discuss a general approach to the computation of the zeros of non-linear polynomial equations with particular emphasis on the lambda matrix eigenproblem. The approach is based on the explicit representation of the (non-unique) slope operator. This operator is then used to generate including iterations for the zeros. The underlying idea is that of the splitting of a multi-variate polynomial.
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    Enclosing the solution set of linear systems with inaccurate data by iterative methods based on incomplete LU-decompositions (1985)
    Springer
    Computing 35 (1985), S. 189-206 
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    ISSN: 1436-5057
    Keywords: 65F10 ; 65G10 ; Interval arithmetic ; linear systems of equations ; iterative solution methods ; incompleteLU-decompositions ; comparison theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Vorgestellt wird eine Klasse von Iterationsverfahren zur Einschließung der Lösungsmenge durch einen Intervallvektor; dabei ist einen×n Intervall-H-Matrix und ein Intervallvektor. Der betrachtete Algorithmus verallgemeinert ein Iterationsverfahren von Meijerink/van der Vorst, das auf einer unvollständigenLU-Zerlegung einerM-MatrixA basiert. Es werden Aussagen über die Durchführbarkeit des Algorithmus, seiner Konvergenzgeschwindigkeit und seiner Einschließungsgüte gemacht. Da das ursprüngliche Verfahren von Meijerink/van der Vorst ein Spezialfall des vorliegenden Algorithmus ist, erhält man damit gleichzeitig seine Durchführbarkeit in der größeren Klasse derH-Matrizen. Als weitere Anwendung auf reelle Matrizen erhält man einen Zusammenhang zwischen demR 1-Faktor (Ortega/Rheinboldt [9]) des ursprünglichen Verfahrens und der zugrundeliegenden IndexmengeP.
    Notes: Abstract We present a class of iterative methods to enclose the solution set by an interval vector;A is varying in ann×n intervalH-Matrix andb is varying in an interval vector . The algorithm taken into consideration generalizes an iterative method of Meijerink/van der Vorst based on an incompleteLU-decomposition of anM-MatrixA. Theorems concerning the feasibility of the algorithm, its rate of convergence and its quality of enclosure are given. Since the original method of Meijerink/van der Vorst is a special case of our algorithm we have thus shown its applicability to the larger class ofH-matrices. Furthermore we relate theR 1-factor (as defined in Ortega/Rheinboldt [9]) of the original method to the underlying setP of indices.
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    Convex spline interpolants with minimal curvature (1985)
    Springer
    Computing 35 (1985), S. 219-229 
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    ISSN: 1436-5057
    Keywords: 65K05 ; 65D07 ; 90C20 ; 41A15 ; Existence conditions ; quadratic programming ; dual optimization problem ; tridiagonal Hessian ; Newton's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Problem, konvexe Interpolationssplines mit minimaler mittlerer Krümmung zu ermitteln, führt auf eine speziell strukturierte quadratische Optimierungsaufgabe. In der vorliegenden Note wird eine zugehörige duale Aufgabe aufgestellt, die ohne Nebenbedingungen auskommt, deren Zielfunktion stückweise quadratisch ist und die daher eine effektive numerische Behandlung erlaubt.
    Notes: Abstract The problem of finding convex spline interpolants with minimal mean curvature leads to a quadratic optimization problem of special structure. In the present note a corresponding dual problem without constraints is derived. Its objective function is piecewise quadratic and therefore admits an effective numerical treatment.
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    Visible surface calculation for complex unstructured polygonal scences (1985)
    Springer
    Computing 35 (1985), S. 231-246 
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    ISSN: 1436-5057
    Keywords: 51N20 ; 68-04 ; 68C05 ; 68C25 ; Visible surface algorithms ; computational geometry ; computer graphics ; computational complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Visible-Surface-Problem besteht darin, die Teilpolygone einer 3-D-Szene aus beliebigen einfachen planaren Polygonen zu bestimmen, die von einem gegebenen Augenpunkt aus sichtbar sind. Der Algorithmus der hier vorgestellt wird, und der für umfangreiche Szenen ausgelegt ist, löst dieses Problem durch implizites Zerlegen bezüglich eines Zellrasters. Die Komplexitätsabschätzung führt zu Aussagen über die günstige Wahl des Gitters und zu der Charakterisierung von Szenenklassen, welche bei praktischen Anwendungen auftreten, und für die der Algorithmus ein lineares Zeit- und Speicherplatzverhalten zeigt.
    Notes: Abstract The visible surface problem is to determine those subpolygons of a 3-D scence of arbitrary simple planar polygons which are visible from a given viewpoint. The algorithm which is presented here, and which is designed for complex scenes solves this problem by an implicit partitioning w.r.t. a raster of cells. The estimation of complexity leads to propositions on the favorable choice of the grid, and to the characterization of classes of scenes, which are relevant for practical applications, and for which the algorithm shows a linear time and space behavior.
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    Symbolic calculation of the trace of the power of a tridiagonal matrix (1985)
    Springer
    Computing 35 (1985), S. 257-268 
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    ISSN: 1436-5057
    Keywords: 05A05 ; Symbolic calculation ; structure and complexity analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird ein Algorithmus vorgeschlagen, der die Spur einer Potenz einer Tridiagonalmatrix berechnet. Er stützt sich auf Techniken, die aus der Strukturanalysis und der Kombinatorik stammen. Die Komplexität des Algorithmus wird analysiert, Verallgemeinerungen und mögliche Anwendungen werden diskutiert.
    Notes: Abstract An algorithm symbolically calculating the trace of the power of a tridiagonal matrix is proposed. The setting is based on techniques developed from structure analysis and combinatorics. The complexity analysis, the extension and the possible applications of this algorithm are also discussed.
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    URL: http://dx.doi.org/10.1007/BF02240193
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    Pseudo-recursive procedures (1985)
    Springer
    Computing 35 (1985), S. 247-256 
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    ISSN: 1436-5057
    Keywords: 68N15 ; 68Q25 ; 68R10 ; Recursion ; Recursive procedures ; activation record ; runtime stack allocation ; dominator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ausgehend von einem entscheidbaren Rekursivitäts-Begriff von Prozeduren (oder Funktionen) in Algol-ähnlichen Programmen definieren wir eine pseudo-rekursive Prozedur als solche, die keine eigene Schachtel (activation record) auf dem Laufzeit-Keller benötigt; sie kann vielmehr innerhalb der Schachtel eines stark-rekursiven (d. h. eines rekursiven aber nicht pseudorekursiven) dynamischen Vorgängers abgelegt werden. Wir stellen einen Algorithmus vor, der jede Prozedur eines Programms entweder als nicht-rekursiv pseudo-rekursiv oder stark-rekursiv einstuft und der jeder pseudo-rekursiven eine geeignete stark-rekursive zuordnet. Anhand dieser Information kann der Übersetzer für jeden Prozedur-Typ eine eigens darauf zugeschnittene Implementierung auswählen.
    Notes: Abstract Based on a decidable notion of recursivity of procedures (or functions) in ALGOL-like programs we define pseudo-recursive procedures to be those that do not need an activation record of their own on the runtime stack; their storage can be allocated within the activation record of a strictly-recursive (i.e. not pseudo-recursive) dynamic predecessor. We present an algorithm that characterizes each procedure of a program as being either non-recursive, pseudo-recursive or strictlyrecursive and associates each pseudo-recursive procedure with one appropriate strictly-recursive one. With this information a better suited implementation technique can be chosen for each type of procedure.
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    Calculation of Minkowski-reduced lattice bases (1985)
    Springer
    Computing 35 (1985), S. 269-276 
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    ISSN: 1436-5057
    Keywords: Primary 10E05 ; 10E25 ; Secondary 65C10 ; Lattice structure ; Minkowski-reduced bases ; reduction of quadratic forms ; random number generation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Bisher gab es nur einen Algorithmus für die Berechnung von Minkowski-reduzierten Gitterbasen bis zur Dimensionn=6 oder höchstens bisn=7. Es wird nun ein neues Verfahren angegeben, das auch für höhere Dimensionen praktikabel ist und wenig Rechenzeit benötigt.
    Notes: Abstract Up to now there has been an algorithm for the calculation of Minkowski-reduced lattice bases to dimensionn=6 or at most ton=7. A new algorithm is presented which is practicable for greater dimensions and requires less computation time.
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    Computing simple bifurcation points using a minimally extended system of nonlinear equations (1985)
    Springer
    Computing 35 (1985), S. 277-294 
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    ISSN: 1436-5057
    Keywords: Primary 65H ; Secondary 47E ; Branch points ; bifurcation points ; extended system ; nonlinear parameter dependent equations ; Newton-like method ; local convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Vorgehensweise zur Berechnung einfacher Bifurkationspunkte nichtlinearer, von einem Parameter abhängender Gleichungssysteme vorgestellt. Zunächst wird das ursprüngliche Gleichungssystem um einen Parameter und zwei Gleichungen erweitert. Das so erhaltene System besitzt eine reguläre Lösung, aus der unmittelbar der gesuchte Bifurkationspunkt abgelesen werden kann. Aufgrund der speziellen Struktur dieses Systems wird ein Newton-ähnliches Verfahren abgeleitet, das ohne die Berechnung zweiter Ableitungen auskommt. Abschließend wird die Wirksamkeit des vorgeschlagenenR-quadratisch konvergenten Verfahrens an einfachen Beispielen demonstriert.
    Notes: Abstract The present paper deals with the computation of simple bifurcation points of nonlinear parameter dependent equations. At first, a minimally extended system of nonlinear equations is constructed by addition of one parameter and two equations. This augmented system has an isolated solution which yields to the simple bifurcation point directly. Using the structural properties of this auxiliary system an adapted Newton-like method is developed not requiring evaluations of second derivatives. Finally, the results of some computer experiments show the efficiency of theR-quadratically convergent method.
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    On the solution of discretized obstacle problems by an adapted penalty method (1985)
    Springer
    Computing 35 (1985), S. 295-306 
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    ISSN: 1436-5057
    Keywords: 65N30 ; Variational inequalities ; finite elements ; penalty methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit wird eine abgestimmte Wahl von Diskretisierungs- und Strafparametern zur Lösung diskretisierter Hindernisprobleme vorgeschlagen. Dabei gelingt es bei Erhaltung der Kondition des Problems, den Fehlereinfluß der Strafmethode auf die Ordnung des Diskretisierungsfehlers zu beschränken. Ferner wird die Konvergenz der diskretisierten Koinzidenzmengen analysiert.
    Notes: Abstract In this paper we present a mutual adjustment for mesh size parameters of the discretization and for penalty parameters. This enables to restrict the error resulting from the penalty technique to the same order as the discretization error without destroying the conditioning of the problem. Furthermore we analyze the convergence of the discrete coincidence set.
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    The polynomial hierarchy and a simple model for competitive analysis (1985)
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    Mathematical programming 32 (1985), S. 146-164 
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    ISSN: 1436-4646
    Keywords: Linear Programming ; NP-Completeness ; Polynomial Hierarchy ; Computational Complexity ; Stackleberg Strategies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The multi-level linear programs of Candler, Norton and Townsley are a simple class of sequenced-move games, in which players are restricted in their moves only by common linear constraints, and each seeks to optimize a fixed linear criterion function in his/her own continuous variables and those of other players. All data of the game and earlier moves are known to a player when he/she is to move. The one-player case is just linear programming. We show that questions concerning only the value of these games exhibit complexity which goes up all levels of the polynomial hierarchy and appears to increase with the number of players. For three players, the games allow reduction of theΣ 2 andΠ 2 levels of the hierarchy. These levels essentially include computations done with branch-and-bound, in which one is given an oracle which can instantaneously solve NP-complete problems (e.g., integer linear programs). More generally, games with (p + 1) players allow reductions ofΣ p andΠ p in the hierarchy. An easy corollary of these results is that value questions for two-player (bi-level) games of this type is NP-hard.
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    An example of irregular convergence in some constrained optimization methods that use the projected hessian (1985)
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    Mathematical programming 32 (1985), S. 232-237 
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    ISSN: 1436-4646
    Keywords: Constrained Optimization ; Reduced Hessian ; Two-step convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we give examples illustrating the behavior of the Coleman-Conn horizontal vertical method and of successive quadratic programming with a Hessian approximation exact on the tangent space of the constraints. One example shows that these methods in general are not one-step superlinearly convergent.
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    A projected lagrangian algorithm for semi-infinite programming (1985)
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    Mathematical programming 32 (1985), S. 337-356 
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    ISSN: 1436-4646
    Keywords: Semi-Infinite Programming ; Descent Algorithm ; Penalty Function ; Lagrangian Function ; Global Convergence ; Second Order Convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A globally convergent algorithm is presented for the solution of a wide class of semi-infinite programming problems. The method is based on the solution of a sequence of equality constrained quadratic programming problems, and usually has a second order convergence rate. Numerical results illustrating the method are given.
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    On the acyclic subgraph polytope (1985)
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    Mathematical programming 33 (1985), S. 28-42 
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    ISSN: 1436-4646
    Keywords: Acyclic Subgraph Problem ; Feedback Arc Set Problem ; Facets of Polyhedra ; Polynomial Time Algorithms ; Weakly Acyclic Digraphs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The acyclic subgraph problem can be formulated as follows. Given a digraph with arc weights, find a set of arcs containing no directed cycle and having maximum total weight. We investigate this problem from a polyhedral point of view and determine several classes of facets for the associated acyclic subgraph polytope. We also show that the separation problem for the facet defining dicycle inequalities can be solved in polynomial time. This implies that the acyclic subgraph problem can be solved in polynomial time for weakly acyclic digraphs. This generalizes a result of Lucchesi for planar digraphs.
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    The cutting stock problem and integer rounding (1985)
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    Mathematical programming 33 (1985), S. 82-92 
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    ISSN: 1436-4646
    Keywords: Cutting Stock Problem ; Knapsack Polyhedron ; Integer Rounding
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An integer programming problem is said to have the integer round-up property if its optimal value is given by the least integer greater than or equal to the optimal value of its linear programming relaxation. In this paper we prove that certain classes of cutting stock problems have the integer round-up property. The proof of these results relies upon the decomposition properties of certain knapsack polyhedra.
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    Extracting embedded generalized networks from linear programming problems (1985)
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    Mathematical programming 32 (1985), S. 11-31 
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    ISSN: 1436-4646
    Keywords: Linear Programming ; Generalized Networks ; Basis Factorization ; Computational Complexity ; Heuristic Algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract If a linear program (LP) possesses a large generalized network (GN) submatrix, this structure can be exploited to decrease solution time. The problems of finding maximum sets of GN constraints and finding maximum embedded GN submatrices are shown to be NP-complete, indicating that reliable, efficient solution of these problems is difficult. Therefore, efficient heuristic algorithms are developed for identifying such structure and are tested on a selection of twenty-three real-world problems. The best of four algorithms for identifying GN constraint sets finds a set which is maximum in twelve cases and averages 99.1% of maximum. On average, the GN constraints identified comprise more than 62.3% of the total constraints in these problems. The algorithm for identifying embedded GN submatrices finds submatrices whose sizes, rows plus columns, average 96.8% of an LP upper bound. Over 91.3% of the total constraint matrix was identified as a GN submatrix in these problems, on average.
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    On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem (1985)
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    Mathematical programming 32 (1985), S. 90-99 
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    ISSN: 1436-4646
    Keywords: Equality Quadratic Program ; Existence and Uniqueness of Solutions ; Null-Space Methods ; Range-Space Methods ; Lagrangian Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present practical conditions under which the existence and uniqueness of a finite solution to a given equality quadratic program may be examined. Different sets of conditions allow this examination to take place when null-space, range-space or Lagrangian methods are used to find stationary points for the quadratic program.
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    Referees 1984 (1985)
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    Mathematical programming 32 (1985), S. 118-121 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    Automatically determining symmetries of partial differential equations (1985)
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    Computing 34 (1985), S. 91-106 
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    ISSN: 1436-5057
    Keywords: 22E99 ; 35-04 ; 35 C 05 ; Symmetry groups ; differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird ein REDUCE-Programm zur Bestimmung der Symmetrien beliebiger Systeme von partiellen Differentialgleichungen beschrieben. Es kann sowohl interaktiv als auch im Batch-Betrieb verwendet werden. In vielen Fällen findet es die volle Symmetriegruppe vollständig automatisch. In einigen anderen Fällen bleiben einige lineare Differentialgleichungen des bestimmenden Systems übrig, dessen Lösung im Augenblick nicht automatisch gefunden werden kann. Falls sie vom Benutzer eingegeben werden, antwortet das System mit den infinitesimalen Generatoren der Symmetriegruppe.
    Notes: Abstract A REDUCE package for determining the group of Lie symmetries of an arbitrary system of partial differential equations is described. It may be used both interactively and in a batch mode. In many cases the system finds the full group completely automatically. In some other cases there are a few linear differential equations of the determining system left the solution of which cannot be found automatically at present. If it is provided by the user, the infinitesimal generators of the symmetry group are returned.
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    An algorithm for computing generalized Euler's transformations of series (1985)
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    Computing 34 (1985), S. 107-116 
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    ISSN: 1436-5057
    Keywords: Primary 65 B 10 ; 6504 ; Euler's transformations ; summation of series ; explicit machine computation and programs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ein Algorithmus für die Berechnung von verallgemeinerten Euler-Transformationen wird vorgelegt. Im Vergleich mit bekannten Algorithmen wurde die Zahl der arithmetischen Operationen etwas vermindert. Numerische Vergleiche mit dem ε-Algorithmus wurden durchgeführt.
    Notes: Abstract An algorithm for computing generalized Euler's transformations of series is established. In comparison with known algorithm, the number of the arithmetic operations results to be slightly reduced. Numerical comparisons with the ε-algorithm are displayed.
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    An intervalal gorithm for solving systems of linear equations to prespecified accuracy (1985)
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    Computing 34 (1985), S. 117-129 
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    ISSN: 1436-5057
    Keywords: 65 G 10 (primary) ; 65 F 05 (secondary) ; Systems of linear equations ; interval arithmetic ; fixed point arithmetic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir beschreiben einen Intervallalgorithmus, der eine gewisse Klasse von linearen Gleichungssystemen löst. Diese Klasse enthält u. a. SystemeAx=b, bei denenA undb ganzzahlige Komponenten haben. Dieser Algorithmus verwendet Festpunktarithmetik und unterscheidet sich von früheren Algorithmen wie folgt. Erstens: Bei Vorgabe der gewünschten absoluten Genauigkeit ε des Ergebnisses benötigt der Algorithmus nur so viel Zwischengenauigkeit wie notwendig, um die Fehlerschranke ε zu erreichen. Zweitens kann der Algorithmus selbststeuernd seine eigenen Parameter dynamisch ändern, um die Rechenzeit zu minimieren.
    Notes: Abstract We describe an interval arithmetic algorithm for solving a special class of simultaneous linear equations. This class includes but is not limited to systemsAx=b whereA andb have integer entries. The algorithm uses fixed point arithmetic, and has two properties which distinguish it from earlier algorithms: given the absolute accuracy ε desired, the algorithm uses only as much precision as needed to achieve it, and the algorithm can adjust its own parameters to minimize computation time.
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    Modifications of some first kind integral equations with logarithmic kernel to improve numerical conditioning (1985)
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    Computing 34 (1985), S. 221-242 
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    ISSN: 1436-5057
    Keywords: 65R20 ; 65F35 ; 45F15 ; 45L10 ; Integral equations ; numerical solution ; matrix norms ; singular values ; condition number ; scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir betrachten ein Paar von Integralgleichungen, das von Symm (1967) und Hsiao & MacCamy (1973) zur Verwendung in verschiedenen Randwertaufgaben hergeleitet worden ist. Wir untersuchen die Matrix, die entsteht, wenn bestimmte Kollokationsmethoden auf die Integralgleichungen angewandt werden. Wir finden, daß diel 2-Konditionszahl der Matrix verkleinert werden kann, wenn drei einfache Modifikationen der Integralgleichungen durchgeführt werden.
    Notes: Abstract We consider a pair of integral equations derived by Symm (1967) and Hsiao & MacCamy (1973) for use in various boundary value problems. We investigate the matrix which results when some collocation methods are applied to these equations. We find that thel 2-condition number of the matrix can be reduced by performing three minor modifications of the integral equations.
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    A systolic array algorithm for the algebraic path problem (shortest paths; Matrix inversion) (1985)
    Springer
    Computing 34 (1985), S. 191-219 
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    ISSN: 1436-5057
    Keywords: 68A05 ; (05C35 ; 05C38 ; 16A78 ; 65F05 ; 68E10 ; C.1.2[processor architectures]: multiple data stream architectures (multiprocessors)-systolic arrays ; G. 1.0 [numerical analysis]: general - parallel algorithms ; G. 1.3 [numerical analysis]: numerical linear algebra - matrix inversion ; G. 2.2 [discrete mathematics]: graph theory - path problems ; B.6.1 [logic design]:design styles - cellular arrays ; B.7.1 [integrated circuits] ; types and design styles - algorithms implemented in hardware ; VLSI (very large scale integration) ; algorithms ; design ; performance ; Algebraic path problem ; shortest paths ; transitive closure ; closed semirings ; Gauß-Jordan elimination
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird dargestellt, wie man den gaus-Jordanschen Eliminationsalgorithmus für das algebraische Wegproblem auf einem hexagonalen systolischen Feld (systolic array) mit einer quadratischen Anzahl einfacher Prozessoren in linearer Zeit ausführen kann. Zu den Anwendungsbeispielen dieses allgemeinen Algorithmus gehört der Warshall-Floyd-Algorithmus zur Berechnung der kürzesten Wegen in einem Graphen oder zur Bestimmung der transitiven Hülle einer Relation sowie der Gauß-Jordansche Eliminationsalgorithmus zur Inversion reeller Matrizen.
    Notes: Abstract It is shown how the Gauß-Jordan Elimination algorithm for the Algebraic Path Problem can be implemented on a hexagonal systolic array of a quadratic number of simple processors in linear time. Special instances of this general algorithm include parallelizations of the Warshall-Floyd Algorithm, which computes the shortest distances in a graph or the transitive closure of a relation, and of the Gauß-Jordan Elimination algorithm for computing the inverse of a real matrix.
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    Centered forms and interval operators (1985)
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    Computing 34 (1985), S. 243-259 
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    ISSN: 1436-5057
    Keywords: 26B99 ; 65H10 ; 47H10 ; 65G10 ; Centered forms ; systems of equations ; interval operators ; fixed-point theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zu einer Funktionf:ℝ n →ℝ m werden zentrische Formen betrachtet. Anschließend wird gezeigt, daß die zentrischen und verallgemeinerten zentrischen Formen der Newton-Transformiertens(x):=x−af(x) bekannte Intervalloperatoren darstellen, welche zur lteration von Intervallfolgen benutzt werden. Aus dieser Tatsache ergeben sich Schlußfolgerungen bezüglich der Existenz eines Fixpunktes und eines „besten Intervalloperators”.
    Notes: Abstract Centered forms of a functionf:ℝ n →ℝ m are considered. It is then pointed out that the centered and generalized centered forms of the Newton-transformations(x):=x−af(x) describe known interval operators which have been introduced for the iteration producing sequences of intervals. This fact implies some conclusions with regard to the existence of a fixpoint or the “best interval operator”.
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    Some old and new Runge-Kutta formulas with stepsize control and their error coefficients (1985)
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    Computing 34 (1985), S. 265-270 
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    ISSN: 1436-5057
    Keywords: Primary 65L05 ; Secondary 34A50 ; Runge-Kutta methods ; error coefficients ; stepsize control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Der Autor leitet eine Variante seiner früheren Runge-Kutta-Formeln 5(6)-ten und 7(8)-ter Ordnung her. Die neuen Formeln sind auch auf Quadratun-Probleme anwendbar. Ihre Fehler-Koeffizienten sind von ungefähr der gleichen Größe wie die der früheren Formeln, aber erheblich kleiner als die entsprechender Formeln von J. H. Vernen.
    Notes: Abstract The author derives a variant of his earlier 5(6)-th and 7(8)-th order Runge-Kutta formulas. The new formulas are also applicable to quadrature problems. Their error coefficients are of about the same magnitude as those of the earlier formulas, but considerably smaller than those of corresponding formulas of J. H. Vermen.
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    Ein Runge-Kutta-Nyström-Formelpaar der Ordnung 11(12) für Differentialgleichungen der Form y″=f(x,y) (1985)
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    Computing 34 (1985), S. 271-282 
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    ISSN: 1436-5057
    Keywords: 65L05 ; Runge-Kutta-Nyström ; y″=f(x, y)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract A new explicit, direct Runge-Kutta-Nyström formula-pair of order 11 (12) with 20 function evaluations per step for initial value problems in ordinary differential equations of second order of the special formy″=f(x, y) is derived. Three numerical examples demonstrate the efficacy of the new formula-pair.
    Notes: Zusammenfassung y″=f(x, y). Es wird erstmals ein explizites, direktes Runge-Kutta-Nyström-Formelpaar der Ordnung 11 (12) mit insgesamt 20f-werten pro Schritt für Anfangswertaufgaben bei gewöhnlichen Differentialgleichungen zweiter Ordnung der speziellen Formy″=f(x, y) aufgestellt. Die Güte dieses Verfahrens wird anhand von drei numerischen Beispielen demonstriert.
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    A converse rule of signs for polynomials (1985)
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    Computing 34 (1985), S. 283-286 
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    ISSN: 1436-5057
    Keywords: 26 C 10 ; 65H05 ; 68C05 ; 68C20 ; Cardano ; Descartes ; rule of signs ; polynomial real root isolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für PolynomeP(x) ist lange bekannt, daß die Zeichenregel von Cardano-Descartes nur obere Schranken für die Anzahl der positiven Nullstellen liefert, ausgenommen die Fälle, in denen ein oder gar kein Vorzeichenwechsel stattfindet, woraus folgt, daßP (x) genau eine oder keine positive Wurzel besitzt. In neuen Methoden zur Trennung der Nullstellen, die bei symbolischer Rechnung von großem Interesse sind, ist die umgekehrte Fragestellung wichtig: Unter welchen Bedingungen hat die Existenz genau einer positiven Wurzel zur Folge, daß bei den Koeffizienten vonP(x) nur ein Zeichenwechsel auftritt? Diese Bedingungen werden in der vorliegenden Arbeit vorgestellt und diskutiert.
    Notes: Abstract Given a polynomialP(x), it is well-known that the Cardano-Descartes rule of signs gives only an upper bound on the number of its positive roots, except in the case in which there is one or no sign variation, where it indicates thatP(x) has one or no positive root(s) respectively. In certain new root isolation methods, of great interest to symbolic mathematical computation, it is important to know under what conditions the existence of one positive root implies thatP(x) presents only one sign variation. These conditions are discussed and presented in this paper.
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    A sweep-plane algorithm for computing the Euler-characteristic of polyhedra represented in Boolean form (1985)
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    Computing 34 (1985), S. 287-302 
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    ISSN: 1436-5057
    Keywords: 15-04 ; 50-04 ; 50B30 ; 52-04 ; Polyhedra ; combinatorial geometry ; computational geometry ; algorithmic geometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir präsentieren einen Algorithmus EULER für die Berechnung der Eulerschen Charakteristik χ(P) beschränkter PolyederP⊂ℝ d . Es wird gezeigt, daß χ(P) durch die lokalen Eigenschaften vonP in seinen Ecken eindeuting bestimmt ist. Deshalb ist es möglich, χ(P) mit Hilfe einer Ebene zu berechnen, die durch den Raum gleitet („sweep-plane”) und die in den Ecken verfügbare Information „sammelt”. Es besteht eine enge Beziehung zu einem früher publizierten Algorithmus für die Berechnung des VolumensV (P) (vgl. [4]). Der Grund liegt darin, daßV und χ beide additive Funktionale sind.
    Notes: Abstract We present an algorithm EULER for the computation of the Euler-characteristic χ(P) of bounded polyhedraP⊂ℝ d . It is first shown that χ(P) is uniquely determined by the local properties ofP at its vertices. It is therefore possible to compute χ(P) using a plane sweeping through ℝ d , collecting the local information available at every vertex. There is a close relationship with an algorithm for the computation of the volumeV (P) published earlier (cf. [4]). The reason is that both ofV and χ are additive functionals.
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    Elimination of redundant operations in relational queries with general selection operators (1985)
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    Computing 34 (1985), S. 303-323 
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    ISSN: 1436-5057
    Keywords: Relational queries ; general selection ; tableau
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Anfragen in relationalen Datenbanken können sogenannte redundante Operationen enthalten, d. h. Operationen, auf die zur Erledigung der Anfrage verzichtet werden kann. Besonders für kostenintensive Operationen, wie Join und Cartesisches Produkt, ist es interessant herauszufinden, ob sie in einem relationalen Ausdruck redundant vorkommen. In dieser Arbeit wird eine Tableauxmethode angewandt, um solche Redundanzen in relationalen Anfragen mit beliebigen Selektionsoperatoren erkennen zu können.
    Notes: Abstract The optimization of relational expressions concerning the elimination of “redundant” operations has been dealt with sofar for a limited class of expressions that puts restrictions on the selection operators involved. We propose a solution for the case of arbitrary selection criteria.
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    On roundoff error distributions in floating point and logarithmic arithmetic (1985)
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    Computing 34 (1985), S. 325-347 
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    ISSN: 1436-5057
    Keywords: 65G ; Key words and phrases ; Roundoff error ; distribution ; floating point arithmetic ; logarithmic computers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Unter Zugrundelegung von sowohl theoretisch als auch empirisch gerechtfertigter Annahmen wird ein stochastisches Modell der Gleitkomma- und der logarithmischen Arithmetik konstruiert. Die Rechtfertigung dieser Annahmen löst offene Fragen bei Hamming (1970) und Bustoz et al. (1979). Diese Modelle werden auf die Fehler von Summen und inneren Produkten angewendet. Es wird ein Vergleich zwischen den Eigenschaften von Gleitkomma- und logarithmischen Rechnern hinsichtlich ihrer Fehleranalyse angestellt. Wir kommen zu dem Schluß, daß der logarithmische Rechner kleinere Fehlerkonfidenzintervalle für die Rundungsfehler aufweist als ein Gleitkommarechner mit der gleichen Wortlänge und dem annähernd gleichen Zahlenbereich.
    Notes: Abstract Probabilistic models of floating point and logarithmic arithmetic are constructed using assumptions with both theoretical and empirical justification. The justification of these assumptions resolves open questions in Hamming (1970) and Bustoz et al. (1979). These models are applied to errors from sums and inner products. A comparison is made between the error analysis properties of floating point and logarithmic computers. We conclude that the logarithmic computer has smaller error confidence intervals for roundoff errors than a floating point computer with the same computer word size and approximately the same number range.
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    Inner product rounding error analysis in the presence of underflow (1985)
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    Computing 34 (1985), S. 365-373 
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    ISSN: 1436-5057
    Keywords: 65G05 ; 64G10 ; Error analysis ; underflow ; sums ; inner products
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die klassische Methode von Wilkinson für die Fehleranalyse von Summen und inneren Produkten wird erweitert auf den Fall des Exponentenunterlaufs. Dies ist wichtig für die Konstruktion von Fehlerschranken von inneren Produkten bei der Berechnung auf Computern, die Exponentenunterlauf nicht anzeigen. Die Methode umfaßt auch den Fall des graduellen Exponentenunterlaufs.
    Notes: Abstract Wilkinson's classical error analysis for sums and inner products is extended to the case where underflow may occur. This is relevant for the construction of rigorous error bounds for an inner product evaluated on computers which do not give underflow messages. The analysis also covers calculations with gradual underflow.
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    URL: http://dx.doi.org/10.1007/BF02251835
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    Probabilistic error analysis of gaussian elimination in floating point and logarithmic arithmetic (1985)
    Springer
    Computing 34 (1985), S. 349-364 
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    ISSN: 1436-5057
    Keywords: Roundoff error ; distribution ; floating point arithmetic ; logarithmic computers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die von Barlow and Bareiss (1985) dargestellten stochastischen Modelle für den Rundungsfehler von Gleitkomma- und logarithmischer Arithmetik werden auf die Fehleranalyse des Gaußschen Eliminationsverfahrens und einiger verwandter Algorithmen angewendet. Diese neue Methode der Fehleranalyse und der von Wilkinson (1963, 1965) gegebenen deterministischen Standard-Fehleranalyse gegenübergestellt.
    Notes: Abstract The probabilistic models for roundoff error in floating point and logarithmic arithmetic discussed in Barlow and Bareiss (1985) are applied to the error analysis of Gaussian elimination and some related algorithms. This new method of error analysis is compared to the standard deterministic error analysis given in Wilkinson (1963, 1965).
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    Some techniques for solving linear equation systems with guarantee (1985)
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    Computing 34 (1985), S. 375-379 
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    ISSN: 1436-5057
    Keywords: 65F10 ; 65G10 ; Linear equations ; iterative methods ; guaranteed accuracy ; interval inclusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Methoden zur Lösung linearer Gleichungssysteme mit Fehlereinschließung werden beschrieben. Sowohl Rechteck-Intervalle als auch Kugeln desR n werden benutzt. Ziel ist es, mit minimalem Aufwand an Rechenzeit Sicherheit in der Lösung zu gewinnen.
    Notes: Abstract Methods are described for solving a system of linear equations with error bounds. Rectangular and spherical intervals ofR n are used combined. The objective is to get guaranteed accuracy with a minimal effort of computing time.
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    Optimizing utilization under response time constraints (1985)
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    Computing 35 (1985), S. 1-12 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden BCMP-Warteschlangennetzwerke betrachtet, die nur aus offenen Ketten bestehen und deren Bedienstationen zustandsunabhängige Bedienraten haben. Für diese Klasse von Netzwerken werden die optimalen Durchsätze der Ketten bestimmt. Als Zielfunktion wird die gewichtete Summe der Stationsauslastungen gewählt. Für jede Kette sind minimale und maximale Durchsätze sowie maximale Antwortzeiten als Nebenbedingungen angebbar.
    Notes: Abstract BCMP queueing networks consisting only of open chains and service centers with state independent service rates are considered. For this class of networks it is shown how to determine the throughputs to optimize a linear objective function which is chosen to be a weighted sum of station utilizations. As restrictions minimal and maximal throughputs and maximal response times are allowed per chain.
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    Ein modifiziertes Newton-Verfahren zur Lösung des Hochrechnungsproblems nach dem Prinzip des minimalen Informationsverlustes (1985)
    Springer
    Computing 35 (1985), S. 51-61 
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    ISSN: 1436-5057
    Keywords: 65D15 ; 90C30 ; 62-07 ; Modified Newton algorithm ; adjustment of microdata ; minimum information loss principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary For the adjustment of microdata based on the minimum information loss principle a nonlinear equation system has to be solved. To solve such a nonlinear system a modified Newton algorithm is proposed, which could reduce the expenses for adjustments of several microdata bases by ca. 75%.
    Notes: Zusammenfassung Für die Hochrechnung einer Mikrodatenbasis nach dem Prinzip des minimalen Informationsverlusts ist ein nichtlineares Gleichungssystem zu lösen. Zur Lösung eines solchen nichtlinearen Systems wird in dem vorliegenden Beitrag ein modifiziertes Newton-Verfahren vorgestellt, das den Aufwand für Hochrechnungen verschiedener Mikrodaten um ca. 75% reduzieren konnte.
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    URL: http://dx.doi.org/10.1007/BF02240146
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    Hierarchical bases of finite-element spaces in the discretization of nonsymmetric elliptic boundary value problems (1985)
    Springer
    Computing 35 (1985), S. 39-49 
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    ISSN: 1436-5057
    Keywords: 65F10 ; 65N20 ; 65N30 ; Elliptic boundary value problems ; finite elements ; conjugate gradient type methods ; fast solvers ; multigrid methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Im Fall positiv definiter und symmetrischer ebener elliptischer Randwertprobleme wachsen die Konditionszahlen der Steifigkeitsmatrizen, die man bei der Diskretisierung solcher Probleme mit der Methode der finiten Elemente erhält, nur quadratisch mit der Anzahl der Verfeinerungsstufen, wenn man die üblichen Knotenbasen der Finite-Element-Räume durch hierarchische Basen ersetzt; siehe [9]. In dieser Arbeit zeigen wir, daß Ergebnisse gleichen Typs für nichtsymmetrische Probleme gelten, und wir beschreiben die interessanten Konsequenzen, die diese Resultate für die Lösung der diskretisierten Probleme mit Krylov-Raum-Methoden haben.
    Notes: Abstract In the case of symmetric and positive definite plane elliptic boundary value problems, the condition numbers of the stiffness matrices arising from finite element discretizations grow only quadratically with the number of refinement levels, if one uses hierarchical bases of the finite element spaces instead of the usual nodal bases; see [9]. Here we show that results of the same type hold for nonsymmetric problems and we describe the interesting consequences for the solution of the discretized problems by Krylov-space methods.
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    On initial value problems in differential-algebraic equations and their numerical treatment (1985)
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    Computing 35 (1985), S. 13-37 
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    ISSN: 1436-5057
    Keywords: 65L05 ; 65L20 ; 94C05 ; 34A08 ; 34A10 ; Multistep method ; initial value problem ; implicit differential equation ; differential-algebraic equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Seit über zehn Jahren werden numerische Integrationsverfahren für Anfangwertaufgaben bei Algebro-Differentialgleichungen (ADGLn) verwendet — mit wechselndem Erfolg. Die notwendige Analyse dieser Methoden wie auch der ADGLn selbst befindet sich jedoch noch in ihrem Anfangsstadium. Ziel der vorliegenden Arbeit sind nicht neue Methoden für ADGLn, sondern die Analyse vorhandener Methoden aus Literatur und Software. Eine Reihe von Aussagen über Stabilität, Konsistenz und Ljapunow-Stabilität verschiedener Methoden wird bewiesen. Speziell erweisen sich eine Trapezregel und gewisse Mehrschrittverfahren als instabil, so daß auf ihnen basierende Codes im allgemeinen versagen werden. Die positiven Ergebnisse können z. B. den praktischen Einsatz von Verfahren höherer Ordnung statt der BDF für geeignete Aufgabenklassen fördern.
    Notes: Abstract For more than ten years numerical integration methods for initial value problems in differential-algebraic equations (DAE's) have been used — with different success. However, the necessary analysis of these methods as well as of the DAE's themselves is only in its beginning. This work does not aim at providing new methods for DAE's, but at analyzing methods known from the literature and software, respectively. A series of results related to the stability, consistency and Liapunov stability of various methods is presented. In particular, a trapezoidal rule as well as certain multistep methods may become unstable, so that codes using these methods will fail in general. The positive results may stimulate the practical use of higher order methods instead of the BDF's for suitable classes of DAE's.
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    Some algorithms for the solution of a class of nonlinear algebraic equations (1985)
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    Computing 35 (1985), S. 63-72 
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    ISSN: 1436-5057
    Keywords: 65J15 ; 47H17 ; 47H07 ; Nonlinear algebraic equations ; Convergence ; Interval arithmetic ; Symmetric single-step method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden einige reelle und intervallmäßige Algorithmen zur numerischen Lösung einer Klasse von nichtlinearen algebraischen Gleichungen beschrieben. Diese Algorithmen basieren auf dem symmetrischen Einzelschrittverfahren [2] und auf Newton-Verfahren nach [10], [11], [8]. Konvergenzsätze und numerische Ergebnisse werden angegeben, die die Effektivität der Algorithmen illustrieren.
    Notes: Abstract Some real and interval algorithms for the numerical solution of a class of nonlinear algebraic equations are described. These algorithms are based upon the symmetric single-step [2] and Newton [10], [11], [8] methods. Convergence theorems and numerical results which illustrate the effectiveness of the algorithms are given.
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    Second-order explicit characteristic difference schemes for quasilinear hyperbolic systems (1985)
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    Computing 35 (1985), S. 85-91 
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    ISSN: 1436-5057
    Keywords: 65M05 ; 65M10 ; 65M25 ; Second order ; characteristic difference schemes ; quasilinear hyperbolic systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir stellen ein Charakteristikenverfahren zweiter Ordnung für die numerische Lösung der Anfangswertaufgabe von quasilinearen hyperbolischen Systemen vor und beweisen die Stabilität des Verfahrens für Systeme mit konstanten Koeffizienten.
    Notes: Abstract We present two-step, second-order explicit characteristic difference schemes for the numerical solution of initialvalue problems for quasilinear hyperbolic system and show that the method is stable for systems with constant coefficients.
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    A theorem for locating eigenvalues (1985)
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    Computing 35 (1985), S. 93-96 
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    ISSN: 1436-5057
    Keywords: 65F15 ; Eigenvalues ; matrix computation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Hauptergebnis dieser Arbeit ist der Satz, daß die Haupt-Minoren der MatrixB-ωA (B symmetrisch und positiv definit,A Hermitesch) ähnliche, Eigenschaften wie Sturmsche Folgen haben. Dieser Satz ist die theoretische Grundlage der Determinanten-Methode für die Lösung des Eigenwert-Problems von gedämpften Systemen, wobei die Fehler einer Arbeit von K. K. Gupta korrigiert werden.
    Notes: Abstract The primary conclusion derived in this paper is that the leading principal minors of matrixB-ωA (whereB is a symmetric positive definite matrix andA is Hermite matrix) have properties similar to those of Sturm sequences, which is the theoretical basis of the Determinant Search Method for solving the eigenvalue-problem of damped structural systems [1]–[5], correcting the errors in a statement given by K. K. Gupta in [1]–[5].
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    Professor R. Albrecht, 60 years (1985)
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    Computing 35 (1985), S. 97-98 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
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    Explicit iterative algorithms to reduce a univariate catastrophe to normal form (1985)
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    Computing 35 (1985), S. 73-83 
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    ISSN: 1436-5057
    Keywords: 58C28 ; 58C27 ; 58C05 ; 68C20 ; Catastrophe theory ; reduction to normal form ; right-equivalence ; computer algebra ; Katastrophentheorie ; Reduktion auf Normalform ; Rechtsäquivalenz ; Computer-Algebra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden Algorithmen zur Lösung eines praktischen Problems der elementaren Katastrophentheorie hergeleitet: die Transformation der Entfaltung einer Singularität, die von einer Zustandsvariablen abhängt, auf Normalform bis zu beliebig vorgegebener Ordnung in den Entfaltungs-parametern. Das Problem wird durch zwei Algorithmen gelöst, die eine einfache explizite Transformation iterieren und daher zur Implementierung mit Hilfe eines Systems der Computer-Algebra geeignet sind. Der Beweis erfolgt durch Ableitung von hinreichenden, Bedingungen für eine Klasse solcher Algorithmen. Komplexität und potentielle Verallgemeinerungen der Algorithmen werden kurz diskutiert.
    Notes: Abstract We derive algorithms to solve a technical problem in elementary catastrophe theory: how to reduce an unfolding of a singularity in a univariate function to normal form up to any given degree in the unfolding parameters. Two algorithms that iterate a simple explicit transformation are proposed, which should be suitable for easy implementation using a computer algebra system. They are proved by deriving sufficient vonditions for a class of such algorithms. The complexity and generalization of the algorithms is discussed briefly.
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    Computing the characteristic polynomial of a tree (1985)
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    Computing 35 (1985), S. 113-125 
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    ISSN: 1436-5057
    Keywords: 05A ; 68B ; Spectra of graphs ; factorizations of the characteristic polynomial of a tree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir stellen einen O(n 3)-Algorithmus zur Berechnung des charakteristischen Polynoms eines Baumes vor. Der Algorithmus liefert dieses Polynom in einer faktorisierten Form, wobei jeder Faktor durch eine gewisse Struktureigenschaft des Baumes bestimmt ist.
    Notes: Abstract We present an O(n 3)-algorithm for computing the characteristic polynomial of a tree in a certain factorized form. Each factor is caused by some structural property of the tree.
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    Time-slot assignment for TDMA-systems (1985)
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    Computing 35 (1985), S. 99-112 
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    ISSN: 1436-5057
    Keywords: 90C08 ; 90C10 ; Matrix decomposition ; time-slot assignment ; assignment problem ; max flow min cost flow problem ; computational complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Bei der Nachrichtenübertragung via Satelliten unter Benützung der TDMA-Technik, wie auch bei mannigfachen anderen technischen Systemen, tritt das Problem auf, daß eine gegebene (n×n)-Matrix mit nichtnegativen Elementen derart in eine Summe von Permutationsmatrizen zu zerlegen ist, daß die Summe der Gewichte minimal wird. Zunächst wird gezeigt, daß eine Optimallösung dieses Problems inO(n 4) Schritten konstruiert werden kann. Dabei werden maximaln 2−2n+2 verschiedene Permutationsmatrizen verwendet. Danach wird kurz die Zerlegung inn Matrizen diskutiert. Dieses Problem ist NP-schwer. Wenn 2n Permutationsmatrizen im vorhinein fixiert werden, kann eine optimale Zerlegung in eine gewichtete Summe dieser Permutationsmatrizen inO(n 3) Zeit durch das Lösen eines linearen Zuordnungsproblems gefunden werden. Dieses letztere Problem kann auf beliebige Boolesche Matrizen verallgemeinert werden. Dies führt dann auf ein maximales Flußproblem mit minimalen Kosten und kann daher ebenfalls durch einen echt-poynomialen Algorithmus gelöst werden.
    Notes: Abstract In satellite communication as in other technical systems using the TDMA-technique (time division multiple access) the problem arises to decompose a given (n×n)-matrix in a weighted sum of permutation matrices such that the sum of the weights becomes minimal. We show at first that an optimal solution of this problem can be obtained inO(n 4)-time using at mostO(n 2) different permutation matrices. Thereafter we discuss shortly the decomposition inO(n) different matrices which turns out to be NP-hard. Moreover it is shown that an optimal decomposition using a class of 2n permutation matrices which are fixed in advance can be obtained by solving a classical assignment problem. This latter problem can be generalized by taking arbitrary Boolean matrices. The corresponding decomposition problem can be transformed to a special max flow min cost network flow problem, and is thus soluble by a genuinely polynomial algorithm.
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    Accurate arithmetic results for decimal data on non-decimal computers (1985)
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    Computing 35 (1985), S. 141-151 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In letzter Zeit wurde eine Methodik entwickelt und implementiert, die die Erzeugung kleinstmöglicher Maschinenzahl-Intervalle für die genauen Ergebnisse verschiedenster vielstufiger mathematischer Operationen gestattet. Diese genauen Ergebnisse beziehen sich jedoch auf die Daten so wie sie im Computer dargestellt sind. In der vorliegenden Note wird gezeigt, wie die Konversion dezimaler Daten in nicht-dezimale Darstellungen mit der mathematischen Operation an den Daten in einen einzigen hoch-genauen Algorithmus zusammengefügt werden kann. Für die Lösung von Systemen linearer Gleichungen wird ein solcher Algorithmus im Detail vorgestellt.
    Notes: Abstract Recently, techniques have been devised and implemented which permit the computation of smallest enclosing machine number interval for the exact results of a good number of highly composite operations. These exact results refer, however, to the data as they are represented in the computer. This note shows how the conversion of decimal data into non-decimal representations may be joined with the mathematical operation on the data into one high-accuracy algorithm. Such an algorithm is explicitly presented for the solution of systems of linear equations.
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    Relative error in floating-point multiplication (1985)
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    Computing 35 (1985), S. 127-139 
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    ISSN: 1436-5057
    Keywords: 65G05 ; 65G10 ; Relative error ; computer arithmetic ; floating point multiplication ; normalization options ; guard digits ; floating point numbers ; floating point precision and significance ; round-off error ; fraction error ; mean and standard deviation of errors ; logarithmically distributed numbers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird ein Modell für den relativen Fehler bei der Gleitkomma-Multiplikation entwickelt unf für verschiedene Kombinationen der Arithmetikparameter stochastisch analysiert. Die Parameter sind die Basis, die Rundungsart, die Anzahl der Schutzstellen, und ob die Normalisierung vor oder nach dem Runden erfolgt. Bei einer angenommenen logarithmischen Verteilung für die Mantisse kommt man zu folgenden Schlüssen: 1. Der durchschnittliche relative Fehler bei der Multiplikation wächst mit der Basis. 2. Dieser Fehler wird minimal für die Basis 2 (am besten mit verborgenem ersten Bit) und recht groß für die Basis 16. 3. Die klassischen Schranken für den relativen Fehler sind pessimistisch. Ihre durchschnittliche Überschätzung wächst mit der Basis.
    Notes: Abstract A model of the relative error in floating point multiplication is developed and is analyzed stochastically for various choices of computer design parameters. These parameters include the base, the type of rounding rule, the number of guard digits, and whether the post-arithmetic normalization shift (if needed) is done before or after rounding. Under the assumption of logarithmic distribution for the fraction (mantissa), the major stochastic conclusions are: 1. The average relative error in multiplication increases as the base increases. 2. This error is minimized by selecting the machine base to be binary (better yet, binary with a hidden bit) and is rather large for machines with base 16. 3. The classical relative error bounds are pessimistic. The average overestimation by those bounds increases as the base increases.
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    An adaptive multi-grid algorithm for the numerical solution of quasilinear potential equations (1985)
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    Computing 35 (1985), S. 307-324 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit soll eine iterative Methode zur numerischen Lösung einer Klasse von quasilinearen Potentialgleichungen mit Hilfe einer adaptiven Mehrgittermethode beschrieben werden. Das Prinzip der Mehrgittertechnik und der Lösungsalgorithmen werden anhand eines Iterationsschrittes des MG-Zyklus vorgestellt. Als Prolongations- und Restriktionsoperatoren, die für den Aufstieg grob-zu-fein bzw. für den Abstieg fein-zu-grob notwendig sind, haben wir eine einfache lineare Interpolation gewählt. Eine elementar durchgeführte Fehlerabschätzung zeigt, daß die von [2] vorgeschlagene Korrekturgleichung modifiziert werden soll, um einen effizienten MG-Algorithmus zu erzielen. Ein anderes Verfahren ist vorgestellt worden. Dies ist nur eine Zweigittermethode, die auf dem gröberen Gitter Linearisierunggen vornimmt. Die numerischen Ergebnisse der vorgestellten Mehrgittermethoden werden am Beispiel der Differentialgleichungen der Minimalflächen präsentiert. Ein Vergleich mit anderen Methoden ist am Beispiel der Minimalflächen durchgeführt.
    Notes: Abstract This paper describes an iterative method for the numerical solution of a class of quasilinear potential equations using an adaptive multi-grid algorithm (MG-algorithm). The method of solution has been illustrated using one iteration step of MG-cycle. The prolongation and restriction operators, which need coarse-to-fine as well as fine-to-coarse grid transfer, have been chosen of very simple linear structure. A simple error estimation has been carried out to show that the correction equation suggested in [2] has to be modified to get an efficient MG-algorithm. Another simple approach has been suggested which is based on a two-level version and uses a linear correction equation only on the coarser grid. We also present computational results of several numerical experiments applied on a specific example of the minimal surface problem. A comparison between our methods and other methods applied on the example of the minimal surface problem has been presented.
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    On the approximate computation of certain strongly singular integrals (1985)
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    Computing 35 (1985), S. 345-353 
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    ISSN: 1436-5057
    Keywords: Primary 65D30 ; Secondary 44A15 ; Strongly singular integrals ; finite-part integrals ; double-pole singularity ; numerical approximation ; quadrature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Integrale mit endlichem Bestandteil, erstmals von Hadamard in Verbindung mit hyperbolischen Partialdifferentialgleichungen eingeführt, finden verschiedene Anwendungen in der Technik. In diesem Artikel werden neue Methoden für die numerische Auswertung von Integralen mit einer Doppelpol-Singularität untersucht.
    Notes: Abstract Finite-part integrals, first introduced by Hadamard in connection with hyperbolic partial differential equations, have been found useful in a number of engineering applications. In this paper we investigate some numerical methods for computing finite-part integrals with a double-pole singularity.
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    Nichtlineare Stabilität und Phasenuntersuchung adaptiver Nyström-Runge-Kutta-Methoden (1985)
    Springer
    Computing 35 (1985), S. 325-344 
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    ISSN: 1436-5057
    Keywords: 65L05 ; Numerical analysis ; Nyström methods ; stiff problems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The stability of adaptive Nyström-Runge-Kutta procedures is studied for a wide class of nonlinear stiff systems of second order differential equations. We show that for a large class of semi-discrete hyperbolic and parabolic problems the restriction of the stepsize is not due to the stiffness of the differential equation. Furthermore we use the scalar test equation $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ to derive conditions which ensure that the numerical forced oscillation is in phase with the analytical forced oscillation. The order of adaptive Nyström-Runge-Kutta methods (with a stability-matrix based on a diagonal Padéapproximation) for which the forced oscillation is in phase with its analytical counterpart cannot be greater than two. This barrier of order is not true forr-stage implicit Nyström methods of orderp=2r.
    Notes: Zusammenfassung Für eine umfangreiche Klasse nichtlinearer steifer Differentialgleichungssysteme zweiter Ordnung wird die Stabilität adaptiver Nyström-Runge-Kutta-Verfahren untersucht. Wir zeigen, daß für eine große Klasse semidiskretisierter hyperbolischer und parabolischer Probleme die Restriktion der Schrittweite unabhängig von der Steifheit des Differentialgleichungssystems ist. Weiterhin verwenden wir die skalare Testgleichung $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ und geben Bedingungen dafür an, daß die numerische erzwungene Schwingung mit der analytischen erzwungenen Schwingung in Phase ist. Die Konsistenzordnung adaptiver Nyström-Runge-Kutta-Verfahren (mit einer Stabilitätsmatrix, die auf einer diagnolen Padé-Approximation beruht), für die die erzwungene Schwingung mit ihrem analytischen Gegenstück in Phase ist, kann nicht größer als zwei sein. Diese Ordnungsbarriere gilt nicht fürr-stufige implizite Nyström-Methoden der Ordnungp=2r.
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    URL: http://dx.doi.org/10.1007/BF02240198
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    Accelerating Krawczyk-like interval algorithms for the solution of nonlinear systems of equations by using second derivatives (1985)
    Springer
    Computing 35 (1985), S. 355-367 
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    ISSN: 1436-5057
    Keywords: 65H10 ; Nonlinear systems of equations ; Krawczyk-like algorithms ; interval arithmetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Kürzlich wurden in mehreren Arbeiten die Eigenschaften von Krawczyk-ähnlichen Intervalliterationsverfahren zur Lösung nichtlinearer Gleichungssysteme untersucht (z. B. [2], [3], [5], [6]). Diese Verfahren konvergieren unter verhältnismäßig schwachen Voraussetzungen gegen eine Lösung, falls eine Anfangseinschließung bekannt ist. In der vorliegenden Arbeit beschreiben wir ein Verfahren, welches die Konvergenz für eine wichtige Klasse von Anwendungen unter Verwendung zweiter partieller Ableitungen verbessert. Dieses Verfahren ist insbesondere für große Systeme interessant, deren Jacobi-Matrix außerhalb der Hauptdiagonalen konstant ist.
    Notes: Abstract Recently the properties of Krawczyk-like iterative interval methods for the solution of systems of nonlinear equations have been discussed in several papers (e.g. [2], [3], [5], [6]). These methods converge to a solution under relatively weak conditions provided an initial inclusion vector is known. In the present paper we describe a method that improves the convergence speed for an important class of problems by using second partial derivatives. This method is particularly interesting for large systems with a Jacobi matrix whose off-diagonal coefficients are all constant.
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    URL: http://dx.doi.org/10.1007/BF02240200
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    Better extrapolation codes (1985)
    Springer
    Computing 35 (1985), S. 369-374 
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    ISSN: 1436-5057
    Keywords: 65L05 ; Ordinary diffeential equations ; extrapolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird gezeigt, wie man den gängigen Codes, die Systeme von gewöhnlichen Differentialgleichungen durch Extrapolation mit variabler Ordnung lösen, eine Formel der Ordnung 1 hinzufügen kann, was das Verhalten der Codes in verschiedener Hinsicht verbessert.
    Notes: Abstract It is shown how to add a formula of order one to the orders available in the popular variable order codes that solve systems of ordinary differential equations by extrapolation. This improves the codes in several ways.
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    URL: http://dx.doi.org/10.1007/BF02240201
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    A remark on Frank matrices (1985)
    Springer
    Computing 35 (1985), S. 375-379 
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    ISSN: 1436-5057
    Keywords: 65F05 ; 65F15 ; 65F35 ; Eigenvalue problem ; test matrix ; mathematical software
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Bei der Analyse und Beurteilung von mathematischer Software sind Testbeispiele mit Informationen über die exakte Lösung von großer Bedeutung. In der vorliegenden Arbeit werden die Eigenschaften einer reellen nichtsymmetrischen Matrix untersucht, die bei der Untersuchung von Verfahren zur Lösung von Eigenwertaufgaben häufig als Modellproblem genommen wird.
    Notes: Abstract Some properties of a matrix are reported which should be useful for creting large test eigenvalue problems with a prescribed condition number and a known solution.
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    URL: http://dx.doi.org/10.1007/BF02240202
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    Human language and computers (1985)
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    Computers and the humanities 19 (1985), S. 77-83 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02259627
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    An investigation of Morton's method to distinguish Elizabethan playwrights (1985)
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    Computers and the humanities 19 (1985), S. 3-21 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02259614
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    Word frequency and text type: Some observations based on the LOB corpus of British English texts (1985)
    Springer
    Computers and the humanities 19 (1985), S. 23-36 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02259615
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    Intelligent knowledge-based systems in archaeology: A computerized simulation of reasoning by means of an expert system (1985)
    Springer
    Computers and the humanities 19 (1985), S. 37-52 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Software review (1985)
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    Computers and the humanities 19 (1985), S. 53-56 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
    Notes: Summary Quibbles aside,Notebook II is a solid program for people who need a database manager for large fields of text. It is efficient, reliable, well documented, and easy to use.WordStar users may well already know about Pro/Tem Software's other programs,Footnote andBibliography.
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    Datcol 4: Interactive data collector for historians (1985)
    Springer
    Computers and the humanities 19 (1985), S. 57-59 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Book reviews (1985)
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    Computers and the humanities 19 (1985), S. 61-67 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    The writer and the computer (1985)
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    Computers and the humanities 19 (1985), S. 85-88 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Computers, bibliography, and foreign language typography (1985)
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    Computers and the humanities 19 (1985), S. 89-95 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Terminology: Teaming upHomo Faber andHomo Linguisticus (1985)
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    Computers and the humanities 19 (1985), S. 103-108 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Book reviews (1985)
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    Computers and the humanities 19 (1985), S. 137-139 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Software reviews (1985)
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    Computers and the humanities 19 (1985), S. 131-136 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Processing emblems with the computer (1985)
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    Computers and the humanities 19 (1985), S. 159-166 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Disambiguation by short contexts (1985)
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    Computers and the humanities 19 (1985), S. 147-157 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Computational lexicography (1985)
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    Computers and the humanities 19 (1985), S. 97-101 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    Machine translation (1985)
    Springer
    Computers and the humanities 19 (1985), S. 109-116 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    URL: http://dx.doi.org/10.1007/BF02259632
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    The “New” logics and natural language processing (1985)
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    Computers and the humanities 19 (1985), S. 123-129 
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    ISSN: 1572-8412
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Media Resources and Communication Sciences, Journalism
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    URL: http://dx.doi.org/10.1007/BF02259634
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