On the convergence of subproper (multi)-splitting methods for solving rectangular linear systems
type: Item
instance of: scholarly article
title: On the convergence of subproper (multi)-splitting methods for solving rectangular linear systems
zbMATH Open document ID: 1139.65023
author: Lijing Lin
author: Yimin Wei
published in: Calcolo
publication date: 2008-06-24T00:00:00Z
review text: The authors discuss iterative methods for solving consistent systems of linear equations \(Ax = b\), where \(A\) is a \(m \times n\) complex matrix. At first a necessary and sufficient condition for the convergence of the stationary iterative process \(x^{(k+1)} = M^+Nx^{(k)} + M^+b\) is derived, where \(A = M-N\) is a subproper splitting of the matrix \(A\) and \(M^+\) denotes the Moore-Penrose inverse of \(M\). Additionally, conditions for the equivalence of the convergence and quotient convergence for the stationary iterative process are given. Finally, the convergence of multi-splitting algorithms for rectangular systems is proved.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 5292375
zbMATH Keywords: Rectangular linear systems
zbMATH Keywords: Iterative method
zbMATH Keywords: Proper splitting
zbMATH Keywords: Subproper splitting
zbMATH Keywords: Regularity
zbMATH Keywords: Hermitian positive semi-definite matrix
zbMATH Keywords: Multisplitting
zbMATH Keywords: Quotient convergence
reviewed by: Michael Jung
MaRDI profile type: Publication
full work available at URL: s10092-008-0141-8
OpenAlex ID: W2099801181
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DOI: 10.1007/S10092-008-0141-8
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description: scientific article; zbMATH DE number 5292375