Convergence for nonnegative double splittings of matrices
type: Item
instance of: scholarly article
title: Convergence for nonnegative double splittings of matrices
zbMATH Open document ID: 1232.65056
author: Juan-Miguel Gracia
published in: Calcolo
publication date: 2011-12-14T00:00:00Z
review text: The authors consider \(n\) by \(n\) systems of linear equations with regular matrix \(A\) and double splittings \(A=P-R-S\) leading to 2-step iterations \(Px^{i+1}=Rx^i+Sx^{i-1}\). They prove convergence theorems like ``a nonnegative double splitting is convergent iff the simple splitting (\(A=P-(R+S)\)) is'' and comparison theorems for different double splittings of the same or of different matrices A. Explicit examples concern \(2\) by \(2\) matrices, there is no result on an advantage of double over simple splittings.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 5988489
zbMATH Keywords: linear systems
zbMATH Keywords: 2-step iterations
zbMATH Keywords: double splittings
zbMATH Keywords: comparison
zbMATH Keywords: convergence
zbMATH Keywords: Jacobi double SOR method
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: s10092-010-0037-2
OpenAlex ID: W1977825977
cites work: A Guide to the Acceleration of Iterative Methods Whose Iteration Matrix is Nonnegative and Convergent
cites work: Q4326384
cites work: Iterative schemes for the neutron diffusion equation.
cites work: Two-sweep iterative methods
cites work: Comparison theorems for weak splittings of bounded operators
cites work: A note on double splittings of different monotone matrices
cites work: Convergence and comparison theorems for double splittings of matrices
cites work: Convergence and comparison results for double splittings of Hermitian positive definite matrices
cites work: Comparisons of nonnegative splittings of matrices
cites work: Q4783139
cites work: Comparison theorems for splittings of matrices
cites work: Q4947421
cites work: Estimation of the Optimum Relaxation Factors in Partial Factorization Iterative Methods
cites work: Q5639278
cites work: On convergence of double splitting methods for non-Hermitian positive semidefinite linear systems
DOI: 10.1007/S10092-010-0037-2
description: scientific article; zbMATH DE number 5988489