Relaxation methods for non-Hermitian linear systems
type: Item
instance of: scholarly article
title: Relaxation methods for non-Hermitian linear systems
zbMATH Open document ID: 0687.65031
DOI: 10.1007/BF03322480
published in: Results in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Many iterative methods for the solution of systems of linear equations \(Ax=b\) arise from a splitting \(A=M-N.\) The authors propose two new possibilities. The basic theorem is the following lemma: If \(I-\omega M_ B\) is nonsingular and if t is an eigenvalue of \((I-\omega M_ B)^{-1}((1-\omega)I+\omega N)\) with eigenvector v, normalized by \(v^*v=1,\) then \(t=((1-\omega)+\omega \eta)/(1-\omega m),\) where \(\eta =v^*Nv,\quad m=v^*M_ Bv.\) The authors study how this lemma can be used to describe regions in the complex plane which contain the spectrum of the corresponding iteration operators.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4126575
zbMATH Keywords: relaxation methods
zbMATH Keywords: non-Hermitian linear systems
zbMATH Keywords: iterative methods
zbMATH Keywords: splitting
author: Wilhelm Niethammer
author: Richard S. Varga
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322480
OpenAlex ID: W2011685366
description: scientific article; zbMATH DE number 4126575