The projection method for solving nonlinear systems of equations under the ''most violated constraint'' control
type: Item
instance of: scholarly article
title: The projection method for solving nonlinear systems of equations under the ''most violated constraint'' control
zbMATH Open document ID: 0584.65023
DOI: 10.1016/0898-1221(85)90019-7
author: J. M. Martínez
publication date: 1985-01-01T00:00:00Z
review text: This paper analyzes an extended version of \textit{S. Kaczmarz}' method [Bull. Inst. Acad. Polon. Sci. A 1937, 355-357 (1937; Zbl 0017.31703)] for solving nonlinear algebraic equations. The method is related to those of \textit{K.-H. Meyn} [Numer. Math. 42, 161-172 (1983; Zbl 0497.65026)] and the reviewer [Indiana Univ. Math. J. 26, 1137-1150 (1977; Zbl 0341.65046) and Numer. Math. 23, 371-385 (1975; Zbl 0303.65046)], but with the major improvement that the equations are treated generally by blocks. It is characterized by the use of local linearization in turn on each block that ``most'' violates the corresponding equations. The method is analyzed theoretically with convergence rate estimates. Some numerical results are also reported.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 3936382
zbMATH Keywords: block version of Kaczmarz's method
zbMATH Keywords: convergence rate estimates
zbMATH Keywords: numerical results
reviewed by: S. F. McCormick
MaRDI profile type: Publication
full work available at URL: 0898-1221(85)90019-7
OpenAlex ID: W2042509817
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3936382