Consistent approximations in Newton-type decomposition methods
type: Item
instance of: scholarly article
title: Consistent approximations in Newton-type decomposition methods
zbMATH Open document ID: 0548.65034
DOI: 10.1007/BF01389589
author: Jochen W. Schmidt
author: Wolfgang Hoyer
author: Christian Haufe
published in: Numerische Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133043
review text: A class of superlinearly convergent Newton-type decomposition methods for solving structured large systems of nonlinear equations recently introduced by the first two authors [Newton-type decomposition methods for equations arising in Network Analysis Z. Angew. Math. Mech. 64, 397- 405 (1984)] is extended in such a way that consistent approximations to the appearing partial and directional derivatives are permitted. As a concrete realization appropriate directional difference quotients are recommended, which reduce the required number of function evaluations and arithmetical operations considerably. Based on suitable consistency conditions, for a general model algorithm local convergence is established with an R-order \(\lambda >1\) depending on the choice of discretization parameters. The paper concludes with an illustrating numerical example.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 3874503
zbMATH Keywords: Newton-type decomposition methods
zbMATH Keywords: large systems
zbMATH Keywords: consistency
zbMATH Keywords: local convergence
zbMATH Keywords: numerical example
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3874503