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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 42 (1983), S. 97-105 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65K05 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Generalized conjugate gradient algorithms which are invariant to a nonlinear scaling of a strictly convex quadratic function are described. The algorithms when applied to scaled quadratic functionsf∶R n →R 1 of the formf(x)=h(F(x)) withF(x) strictly convex quadratic andh∈C 1(R 1) an arbitrary strictly monotone functionh generate the same direction vectors as for the functionF without perfect steps.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 51 (1987), S. 429-439 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F05 ; CR: G1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we consider an extension to nonlinear algebraic systems of the class of algorithms recently proposed by Abaffy, Broyden and Spedicato for general linear systems. We analyze the convergence properties, showing that under the usual assumptions on the function and some mild assumptions on the free parameters available in the class, the algorithm is locally convergent and has a superlinear rate of convergence (per major iteration, which is computationally comparable to a single Newton's step). Some particular algorithms satisfying the conditions on the free parameters are considered.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Annals of the Institute of Statistical Mathematics 42 (1990), S. 187-201 
    ISSN: 1572-9052
    Keywords: Linear systems ; direct methods ; scaling of equations ; conjugate direction methods ; biorthogonalization methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A generalization of the class of direct methods for linear systems recently introduced by Abaffy, Broyden and Spedicato is obtained by applying these algorithms to a scaled system. The resulting class contains an essentially free parameter at each step, giving a unified approach to finitely terminating methods for linear systems. Various properties of the generalized class are presented. Particular attention is paid to the subclasses that contain the classic Hestenes-Stiefel method and the Hegedus-Bodocs biorthogonalization methods.
    Type of Medium: Electronic Resource
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  • 4
    Title: ABS Projection Algorithms: Mathematical techniques for linear and nonlinear equations
    Author: Abaffy, Jozsef
    Contributer: Spedicato, Emilio
    Publisher: Chichester :Ellis Horwood,
    Year of publication: 1989
    Pages: 220 S.
    Series Statement: Mathematics and its applications
    Type of Medium: Book
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