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  • Articles  (97)
  • Articles: DFG German National Licenses  (97)
  • Springer  (97)
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  • Mathematics  (97)
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  • Articles  (97)
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  • 1
    Electronic Resource
    Electronic Resource
    Matrix orthogonal Laurent polynomials and two-point Padé approximants (1992)
    Springer
    Numerical algorithms 3 (1992), S. 201-209 
    Details
    ISSN: 1572-9265
    Keywords: AMS 15 ; 41 ; Orthogonal polynomials ; Laurent polynomials ; T-fractions ; Padé approximants
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper is concerned with double sequencesC={C n} n =−∞/∞ of Hermitian matrices with complex entriesC n ∈M s×s ) and formal Laurent seriesL 0(z)=−Σ k=1 ∞ C −k z k andL ∞(z)=Σ k=0 ∞ C k z −k . Making use of a Favard-type theorem for certain sequences of matrix Laurent polynomials which was obtained previously in [1] we can establish the relation between the matrix counterpart of the so-calledT-fractions and matrix orthogonal Laurent polynomials. The connection with two-point Padé approximants to the pair (L 0,L ∞) is also exhibited proving that such approximants are Hermitian too. Finally, error formulas are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02141929
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  • 2
    Electronic Resource
    Electronic Resource
    On extrapolation of Jagerman and Stetter rules (1992)
    Springer
    Numerical algorithms 3 (1992), S. 211-222 
    Details
    ISSN: 1572-9265
    Keywords: Weight function ; integration rules ; extrapolation methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper quadrature rules introduced by Jagerman [1] and Stetter [2] are considered and asymptotic expansions for the error given. This allows to make use of the Romberg extrapolation process. Such rules can be viewed as generalizations of the well-known mid-point rule. Thus, numerical examples comparing these rules are finally presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02141930
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  • 3
    Electronic Resource
    Electronic Resource
    Chapter 7 DEA multiplier analytic center sensitivity with an illustrative application to independent oil companies (1996)
    Springer
    Annals of operations research 66 (1996), S. 163-177 
    Details
    ISSN: 1572-9338
    Keywords: Efficiency sensitivity ; interior point algorithm ; analytic centers ; potential data errors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The setE of extreme points which are also efficient are of basic importance in defining the efficiency frontier, from which the observations for all other DMUs are evaluated in DEA. A significant question which we address is “What variations in the data can be tolerated before the membership inE is changed?” This topic is explored using (1) a simple illustrative example, and (2) production data for 30 independent oil companies during the period 1983–1985. Data were allowed to vary simultaneously for all observations and in different subsets determined by random drawings of data for points both inE and not inE. The results were found to be robust in this study, thereby lending further support to earlier studies which also found these classifications into efficient and inefficient performers to be robust in DEA. Technical developments for these new methods of sensitivity analysis are supplied. These developments feature an application of analytic center (interior point) algorithms which ensure that the Strong Complementary Slackness Condition (SCSC) is fulfilled. The solutions satisfy a mathematical condition called “centrality”. Generally, the solutions are at interior points calledanalytic centers. At these interior points, continuity of the input-output ratios ensures that DMUs inE remain inE for at least small relative variations in the data, while empirically these properties have been found to extend to much larger variations in the data sets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187299
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  • 4
    Electronic Resource
    Electronic Resource
    Chapter 6 On the construction of strong complementarity slackness solutions for DEA linear programming problems using a primal-dual interior-point method (1996)
    Springer
    Annals of operations research 66 (1996), S. 139-162 
    Details
    ISSN: 1572-9338
    Keywords: Primal-dual interior-point algorithm ; strong complementarity slackness ; analytic center of the solution set ; DEA
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A novel approach for solving the DEA linear programming problems using a primaldual interior-point method is presented. The solution found by this method satisfies the Strong Complementarity Slackness Condition (SCSC) and maximizes the product of the positive components among all SCSC solutions. The first property is critical in the use of DEA and the second one contributes significantly to the reliability of the solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187298
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  • 5
    Electronic Resource
    Electronic Resource
    The time path of the marginal cost of oil: The turning point and the subsequent upward drift (1996)
    Springer
    Annals of operations research 68 (1996), S. 409-422 
    Details
    ISSN: 1572-9338
    Keywords: Depletable non-renewable resources ; marginal cost ; technological progress ; depletion of reserves ; constrained least squares regression
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The gradual exhaustion of existing deposits of a depletable non-renewable resource such as oil tends to shift the supply price curve of the resource upwards, increasing its marginal cost. Advances in technologies for exploration and production act as a brake on such upward shifts. Thus, there is a tug-of-war between the gradual exhaustion of existing deposits and technological progress. Using a recently developed constrained least-squares regression technique, we demonstrate that technological progress was the dominant force of the two during the first part of this century, causing a secular drop in marginal costs, but that this situation eventually was reversed, and that the gradual exhaustion of deposits gained the upper hand, causing marginal costs to increase. The turning point occurred around 1971–72. We also discuss the forecasting of the possible current upward drift of marginal costs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02207224
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  • 6
    Electronic Resource
    Electronic Resource
    Duality and finite spaces (1990)
    Springer
    Order 6 (1990), S. 401-408 
    Details
    ISSN: 1572-9273
    Keywords: 55M05 ; 55N30 ; 06A10 ; Finite spaces ; sheaf cohomology ; dualizing complex ; geometric realization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Using that finite topological spaces are just finite orders, we develop a duality theory for sheaves of Abelian groups over finite spaces following closely Grothendieck's duality theory for coherent sheaves over proper schemes. Since the geometric realization of a finite space is a polyhedron, we relate this duality with the duality theory for Abelian sheaves over polyhedra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00346134
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  • 7
    Electronic Resource
    Electronic Resource
    Cooperative solutions in an economic growth game (1998)
    Springer
    Annals of operations research 84 (1998), S. 209-230 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A differential game with workers and capitalists as players is considered. The players distribute the output of an economy and make decisions about their consumption and investment. They wish to reach at least a proposed final capital. The paper studies the non-dominated payoffs and the associated strategies in the case of the players cooperating and synchronizing their actions. The Pareto solutions are compared with the Nash equilibria.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018940920851
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  • 8
    Electronic Resource
    Electronic Resource
    Some results about numerical quadrature on the unit circle (1996)
    Springer
    Advances in computational mathematics 5 (1996), S. 297-328 
    Details
    ISSN: 1572-9044
    Keywords: Distribution functions ; integration rules ; interpolation nodes ; Szegö polynomials ; 41 ; 65D
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, quadrature formulas on the unit circle are considered. Algebraic properties are given and results concerning error and convergence established. Finally, numerical experiments are carried out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02124749
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  • 9
    Electronic Resource
    Electronic Resource
    Examples of Minimal Unit Vector Fields (2000)
    Springer
    Annals of global analysis and geometry 18 (2000), S. 385-404 
    Details
    ISSN: 1572-9060
    Keywords: geodesic ; normal ; strongly normal and minimal unit vector fields
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We provide a series of examples of Riemannian manifoldsequipped with a minimal unit vector field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006788819180
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  • 10
    Electronic Resource
    Electronic Resource
    On the Starting Algorithms for Fully Implicit Runge-Kutta Methods (2000)
    Springer
    BIT 40 (2000), S. 685-714 
    Details
    ISSN: 1572-9125
    Keywords: Stiff initial value problems ; implicit Runge-Kutta methods ; solution of stage equations ; starting algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the behavior of starting algorithms to solve the algebraic equations of stages arising when fully implicit Runge-Kutta methods are applied to stiff initial value problems. The classical Lagrange extrapolation of the internal stages of the preceding step and some variants thereof that do not require any additional cost are analyzed. To study the order of the starting algorithms we consider three different approaches. First we analyze the classical order through the theory of Butcher's series, second we derive the order on the Prothero and Robinson model and finally we study the stiff order for a general class of dissipative problems. A detailed study of the orders of some starting algorithms for Gauss, Radau IA-IIA, Lobatto IIIA-C methods is also carried out. Finally, to compare the most relevant starting algorithms studied here, some numerical experiments on well known nonlinear stiff problems are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022340401909
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