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  • Articles  (39)
  • Articles: DFG German National Licenses  (39)
  • CR: 5.15  (37)
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  • Springer  (39)
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  • 1980-1984  (39)
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  • Mathematics  (39)
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  • Articles  (39)
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  • Articles: DFG German National Licenses  (39)
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  • Springer  (39)
  • American Chemical Society (ACS)
  • Periodicals Archive Online (PAO)
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  • 1
    Electronic Resource
    Electronic Resource
    Sublinear convergence of the Chord method at singular points (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 147-154 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65H10 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We give sufficient conditions for convergence of the chord method for a class of singular problems. The rate of convergence is sublinear.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395307
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  • 2
    Electronic Resource
    Electronic Resource
    A method of solving nonlinear variational problems by nonlinear transformation of the objective functional. Part I (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 59-82 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65K10 ; CR: 5.15 ; 5.41
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A general globally convergent iterative method for solving nonlinear variational problems is introduced. The method is applied to a temperature control problem and to the minimal surface problem. Several aspects of finite element implementation of the method are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389638
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  • 3
    Electronic Resource
    Electronic Resource
    Das modifizierte Newton-Verfahren in verallgemeinerten Banach-Räumen (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 91-104 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65J15 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A Newton-Kantorowitsch-analysis of the modified Newton's method in generalized Banach-spaces is given. The application of generalized norms — mappings from a linear space into an ordered Banach-space — improves convergence- and existence results as well as error estimates compared with the real-norm theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389640
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  • 4
    Electronic Resource
    Electronic Resource
    A general convergence theorem for the reduced gradient method (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 241-247 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 90C30 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Consider the problem of minimizing a real function subject to linear equality constraints and to nonnegativity bounds on the variables. A convergence theorem is established for a general algorithm model based on the reduced gradient method. The most meaningful assumptions that are made, concern two crucial points: the choice of the independent variables and that of the search direction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390125
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  • 5
    Electronic Resource
    Electronic Resource
    Error bounds of Newton type process on Banach spaces (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 175-193 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) (1980) ; Primary 65J05, 65J15 ; Secondary 47H10 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For solving a nonlinear operator equationF(x)=0 in Banach spaces, the Newton's method or Newton type methods are important numerical techniques. We use the properties of real equationt=Φ(t) majorizing an operator equationx=Gx to find a fixed point ofG as a solution of equationF(x)=0. Various type of operatorsG are considered in this paper. For a nonlinear operatorG, we would find a real function Φ majorizing the operatorG and it will be related to a rate of convergence $$\omega (r) = \frac{{r^2 }}{{2(r^2 + d)^{1/2} }}.$$ It follows thatG has a fixed point as a solution ofF(x)=0. Practical limitations of error bounds like as in Potra and Pták [5] are discribed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408692
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  • 6
    Electronic Resource
    Electronic Resource
    Some convergence results for asynchronous algorithms (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 325-340 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary In this paper we present convergence results for the asynchronous algorithms based essentially on the notion of classical contraction. We generalize, in particular, all convergence results for those algorithms which are based on the vectorial norm hypothesis, in wide spread use recently. Certain problems, for which the vectorial norm hypothesis can be difficult or even impossible to verify, can nontheless be tackled within the scope of the classical contraction that we adopte.
    Notes: Resumé Nous présentons dans cet article des résultats de convergence des algorithmes asynchrones basés essentiellement sur la notion classique de contraction. Nous généralisons, en particulier, tous les résultats de convergence de ces algorithmes qui font l'hypothèse de contraction en norme vectorielle qui récemment a été très souvant utilisée. Par ailleurs, l'hypothèse de contraction en norme vectorielle peut se trouver difficile, voire impossible à vérifier pour certains problèmes qui peuvent être cependant abordés dans le cadre de la contraction classique que nous adoptons.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407866
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  • 7
    Electronic Resource
    Electronic Resource
    Local convergence analysis for partitioned quasi-Newton updates (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 429-448 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65K05 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper considers local convergence properties of inexact partitioned quasi-Newton algorithms for the solution of certain non-linear equations and, in particular, the optimization of partially separable objective functions. Using the bounded deterioration principle, one obtains local and linear convergence, which impliesQ-superlinear convergence under the usual conditions on the quasi-Newton updates. For the optimization case, these conditions are shown to be satisfied by any sequence of updates within the convex Broyden class, even if some Hessians are singular at the minimizer. Finally, local andQ-superlinear convergence is established for an inexact partitioned variable metric method under mild assumptions on the initial Hessian approximations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407874
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  • 8
    Electronic Resource
    Electronic Resource
    Bisection is optimal (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 111-117 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We seek an approximation to a zero of a continuous functionf:[a,b]→ℝ such thatf(a)≦0 andf(b)≧0. It is known that the bisection algorithm makes optimal use ofn function evaluations, i.e., yields the minimal error which is (b−a)/2 n+1, see e.g. Kung [2]. Traub and Wozniakowski [5] proposed using more general information onf by permitting the adaptive evaluations ofn arbitrary linear functionals. They conjectured [5, p. 170] that the bisection algorithm remains optimal even if these general evaluations are permitted. This paper affirmatively proves this conjecture. In fact we prove optimality of the bisection algorithm even assuming thatf is infinitely many times differentiable on [a, b] and has exactly one simple zero.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459080
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  • 9
    Electronic Resource
    Electronic Resource
    On a numerical treatment for the curve-tracing of the homotopy method (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 323-329 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65K05 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A Newton-like iteration scheme is proposed for the tracing of an implicitly defined smooth curve. This scheme originates from the study of the continuous Newton-Raphson method for underdetermined systems and, hence, inherits the characteristic property of orthogonality. Its domain of attraction is formed and makes it possible to trace this curve more efficiently.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389577
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  • 10
    Electronic Resource
    Electronic Resource
    A generalized conjugate gradient algorithm for minimization (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 223-230 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65K05 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A generalized conjugate gradient algorithm which is invariant to a nonlinear scaling of a strictly convex quadratic function is described, which terminates after at mostn steps when applied to scaled quadratic functionsf: R n →R1 of the formf(x)=h(F(x)) withF(x) strictly convex quadratic andh∈C 1 (R1) an arbitrary strictly monotone functionh. The algorithm does not suppose the knowledge ofh orF but only off(x) and its gradientg(x).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396318
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