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  • Articles  (4)
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  • Springer  (4)
  • American Chemical Society
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  • Blackwell Publishing Ltd
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  • 1990-1994
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  • Mathematics  (4)
  • 1
    Electronic Resource
    Electronic Resource
    Approximation of time-dependent free boundaries (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 179-199 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; Primary 65N30 ; Secondary 35R35 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Two problems are considered in the paper: the first of them is connected with elliptic variational inequalities and consists in developing a moving obstacle algorithm for approximating the unknown free boundary; the other problem is linked with numerical solution of the Stefan problem, which is formulated in the similar way as in the elliptic case. Some computational aspects are also discussed in the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400538
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  • 2
    Electronic Resource
    Electronic Resource
    Constructive characterization ofA-stable approximations to exp(z) and its connection with algebraically stable Runge-Kutta methods (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 247-258 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65L05 CR ; 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary All rational approximations to exp(z) of order ≧2m−β (m denotes the maximal degree of nominator and denominator) are given by a closed formula involving β real parameters. Using the theory of order stars [9], necessary and sufficient conditions forA-stability (respectivelyI-stability) are given. On the basis of this characterization relations between the concepts ofA-stability and algebraic stability (for implicit Runge-Kutta methods) are investigated. In particular we can partly prove the conjecture that to any irreducibleA-stableR(z) of oderp≧0 there exist algebraically stable Runge-Kutta methods of the same order withR(z) as stability function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408698
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  • 3
    Electronic Resource
    Electronic Resource
    Optimally scaled matrices, necessary and sufficient conditions (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 239-245 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65F35 CR ; 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We shall in this paper consider the problem of determination a row or column scaling of a matrixA, which minimizes the condition number ofA. This problem was studied by several authors. For the cases of the maximum norm and of the sum norm the scale problem was completely solved by Bauer [1] and Sluis [5]. The condition ofA subordinate to the pair of euclidean norms is the ratio Λ/λ, where Λ and λ are the maximal and minimal eigenvalue of (A H A)1/2 respectively. The euclidean case was considered by Forsythe and Strauss [3]. Shapiro [6] proposed some approaches to a numerical solution in this case. The main result of this paper is the presentation of necessary and sufficient conditions for optimal scaling in terms of maximizing and minimizing vectors. A uniqueness proof for the solution is offered provided some normality assumption is satisfied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408697
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  • 4
    Electronic Resource
    Electronic Resource
    Zur effektiven Lösung von booleschen, quadratischen Optimierungsproblemen (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 99-109 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65K05 CR ; 5.41
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Zusammenfassung Es wird die zum booleschen, quadratischen Optimierungsproblem duale Aufgabe untersucht. Ihr optimaler Zielfunktionswert liefert wesentlich schärfere Schranken für den branch and bound Prozeß als die bisher verwendeten.
    Notes: Summary The dual of the boolean quadratic programming problem is considered. The optimal value of their objective function gives bounds for the branch and bound process, which seem to be better then known from other autors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459079
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