On nonlinear SOR-like methods. II: Convergence of the SOR-Newton method for mildly nonlinear equations
type: Item
instance of: scholarly article
title: On nonlinear SOR-like methods. II: Convergence of the SOR-Newton method for mildly nonlinear equations
zbMATH Open document ID: 0881.65041
DOI: 10.1007/BF03167313
author: Kazuo Ishihara
author: Yoshiaki Muroya
author: Tetsuro Yamamoto
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 1997-12-07T00:00:00Z
review text: [For part I see the third author ibid. 14, No. 1, 87-97 (1997; Zbl 0881.65038).] The nonlinear Gauss-Seidel method is often performed in a way such that the auxiliary one-dimensional problems are only approximately solved. From the theory of iterative methods for linear equations it is natural to multiply the one-dimensional corrections with overrelaxation factors \(\omega>1\). Local convergence results are derived and applied to systems of equations which arise from the discretization of the semilinear elliptic equation \(\Delta u+ f(u)=0\).
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1054331
zbMATH Keywords: nonlinear SOR-like methods
zbMATH Keywords: SOR-Newton method
zbMATH Keywords: local systems
zbMATH Keywords: nonlinear Gauss-Seidel method
zbMATH Keywords: iterative methods
zbMATH Keywords: systems
zbMATH Keywords: semilinear elliptic equation
reviewed by: D. Braess
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03167313
OpenAlex ID: W2064522561
description: scientific article; zbMATH DE number 1054331