Convergence and quotient convergence of iterative methods for solving singular linear equations with index one
type: Item
instance of: scholarly article
title: Convergence and quotient convergence of iterative methods for solving singular linear equations with index one
zbMATH Open document ID: 1161.65026
author: Lijing Lin
author: Yimin Wei
author: Nai-Min Zhang
published in: Linear Algebra and its Applications
publication date: 2009-02-25T00:00:00Z
review text: Let \(A\) be a matrix with index \(1\). The solution of a linear system \(Ax=b\) is possible in the quotient space \(\mathbb R^n/{N}(A)\) if \(N(A)\) denotes the kernel and \(b\) lies in the range of \(A\). Iterative solvers are considered modulo \({N}(A)\). Convergence to the solution of minimal norm is of special interest. The use of the group inverse admits a formal generalization of known convergence results for linear iterative methods.
reviewed by: D. Braess
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 5518779
zbMATH Keywords: singular linear equations
zbMATH Keywords: iterative methods
zbMATH Keywords: group inverse
zbMATH Keywords: index one
zbMATH Keywords: Markov chain
zbMATH Keywords: quotient convergence
MaRDI profile type: Publication
full work available at URL: j.laa.2008.06.019
OpenAlex ID: W2076900283
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DOI: 10.1016/J.LAA.2008.06.019
description: scientific article; zbMATH DE number 5518779