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  • Articles  (8)
  • AMS(MOS)  (8)
  • Springer  (8)
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  • 2005-2009
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  • 1980-1984  (8)
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  • 1982  (4)
  • 1980  (4)
  • Mathematics  (8)
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  • Articles  (8)
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  • Springer  (8)
  • American Chemical Society
  • American Institute of Physics
  • Annual Reviews
  • Blackwell Publishing Ltd
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  • 2005-2009
  • 1990-1994
  • 1980-1984  (8)
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  • Mathematics  (8)
  • 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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  • 5
    Electronic Resource
    Electronic Resource
    Une méthode multipas implicite-explicite pour l'approximation des équations d'évolution paraboliques (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 257-276 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65M10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Résumé Considérons une équation d'évolution parabolique linéaire associée à un opérateur linéaireA(t) dépendant du tempst. Nous développons dans cet article une méthode de discrétisation, basée sur les méthodes linéaires à pas multiples, traitant de manière implicite une partie de l'opérateurA(t) indépendante du temps, l'autre partie est traitée de manière explicite. Nous étudions la stabilité et la convergence de cette méthode.
    Notes: Summary Let us consider a linear parabolic equation which is associated with a time dependent operatorA(t). In this paper, we present a method, which is founded on linear multistep methods, which discretize a time-independent part of the operatorA(t) in an implicit way, and the other part in an explicit way. We study stability and convergence for this method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396412
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  • 6
    Electronic Resource
    Electronic Resource
    On the efficient solution of nonlinear finite element equations I (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 277-291 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N30 ; 65H10 ; 65K10 ; CR: 5.17, 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary On the efficient solution of nonlinear finite element equations. A fast numerical method is presented for the solution of nonlinear algebraic systems which arise from discretizations of elliptic boundary value problems. A simplified relaxation algorithm which needs no information about the Jacobian of the system is combined with a correspondingly modified conjugate gradient method. A global convergence proof is given and the number of operations required is compared with that of other algorithms which are equally applicable to a large class of problems. Numerical results verify the efficiency for some typical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396413
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  • 7
    Electronic Resource
    Electronic Resource
    Mixed finite elements in ℝ3 (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 315-341 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present here some new families of non conforming finite elements in ℝ3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396415
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  • 8
    Electronic Resource
    Electronic Resource
    Concerning the solution set ofAx=b whereP≦A≦Q andp≦b≦q (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 355-359 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65F99 ; CR ; 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary LetP≦Q ben×n real matrices so that ifP≦A≦Q for some matrixA, thenA is nonsingular. Letp andq ben-dimensional real column vectors. This paper determines the set of all solutionsx to the equationAx=b for allA andb so thatP≦A≦Q andp≦b≦q.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396417
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