The local convergence of ABS methods for nonlinear algebraic equations
type: Item
instance of: scholarly article
title: The local convergence of ABS methods for nonlinear algebraic equations
zbMATH Open document ID: 0609.65038
DOI: 10.1007/BF01397545
author: Aurél Galántai
author: E. Spedicato
author: József Abaffy
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133204
review text: The class of algorithms for linear systems recently proposed by the first author, \textit{C. Broyden} and the third author [ibid. 45, 361-376 (1984; Zbl 0535.65009)] is extended to nonlinear algebraic systems. The extended class contains as special cases the algorithms of Brown, Brent and the class proposed by Gay. The local convergence properties are analyzed showing that, under the usual assumptions on the function and mild assumptions on the free parameters, the algorithms are locally convergent with a superlinear Q-rate of convergence (usually quadratic) per major iteration, which is computationally equivalent to a Newton step.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 3986544
zbMATH Keywords: ABS class
zbMATH Keywords: iterative processes
zbMATH Keywords: nonlinear algebraic systems
zbMATH Keywords: local convergence
zbMATH Keywords: superlinear Q-rate of convergence
MaRDI profile type: Publication
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OpenAlex ID: W2074033977
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description: scientific article; zbMATH DE number 3986544