Subspace projection variants on Newton's method
type: Item
instance of: scholarly article
title: Subspace projection variants on Newton's method
zbMATH Open document ID: 0821.65030
DOI: 10.1016/0898-1221(94)90062-0
publication date: 1995-09-27T00:00:00Z
review text: The paper deals with a variant of Newton's method for solving a not necessarily square system \(F(x) = 0\) of nonlinear equations. The basic iteration step \(x_{n+1} = x_ n + Y_ ny_ n\) requires a solution of the square linear system \(J_ ny_ n = - F(x_ n)\) with \(J_ n = F'(x_ n) Y_ n\), where \(F'(x_ n)\) denotes the Jacobian and \(Y_ n\) is an appropriate right preconditioner of the Jacobian. This class includes the so-called angle method by \textit{D. D. Georg} and \textit{R. F. Keller} [Comput. Math. Appl. 2, 225-232 (1976; Zbl 0375.65027)] as well as the classical Newton method. The method can be seen as a projection method on a (possibly lower-dimensional) subspace. The convergence of the method for affine problems and the local convergence for nonlinear problems are analyzed and numerical examples are given.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 579946
zbMATH Keywords: nonlinear system
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: Newton's method
zbMATH Keywords: preconditioner
zbMATH Keywords: angle method
zbMATH Keywords: projection method
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
author: Thomas S. Shores
author: C. A. Tiahrt
reviewed by: Walter Zulehner
MaRDI profile type: Publication
full work available at URL: 0898-1221(94)90062-0
OpenAlex ID: W1975484477
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published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 579946