Some comparison theorems for nonnegative splittings of matrices
type: Item
instance of: scholarly article
title: Some comparison theorems for nonnegative splittings of matrices
zbMATH Open document ID: 0803.65035
DOI: 10.1007/BF01385750
published in: Numerische Mathematik
publication date: 1995-01-02T00:00:00Z
full work available at URL: https://eudml.org/doc/133733
review text: In an earlier paper [Lin. Algebra Appl. 154-156, 433-455 (1991; Zbl 0732.65024)], the author gave some theorems on the comparison of asymptotic convergence rates of nonnegative splittings of matrices which extended the result of \textit{V. A. Miller} and \textit{M. Neumann} [Numer. Math. 47, 427-434 (1985; Zbl 0569.65027)]. This paper extends these results and gives theorems concerning two splittings \(A = M_ 1 - N_ 1\), \(A = M_ 2 - N_ 2\) of the square matrix \(A \in \mathbb{C}^{n \times n}\). The splitting is nonnegative if \(M^{-1}N\) is nonnegative. The new results involve the matrices \(A^{-1} M_ 1\), \(M_ 1A^{-1}\), \(A^{- 1} M_ 2\), \(M_ 2 A^{-1}\).
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 569156
zbMATH Keywords: iterative methods
zbMATH Keywords: asymptotic convergence rates
zbMATH Keywords: nonnegative splittings
author: Yongzhong Song
reviewed by: Adrian Swift
MaRDI profile type: Publication
cites work: Factorization iterative methods, M-operators and H-operators
cites work: On Sparse Block Factorization Iterative Methods
cites work: Q3943082
cites work: Comparisons of regular splittings of matrices
cites work: Comparisons of weak regular splittings and multisplitting methods
cites work: A note on comparison theorems for nonnegative matrices
cites work: A Simple Approach to the Perron-Frobenius Theory for Positive Operators on General Partially-Ordered Finite-Dimensional Linear Spaces
cites work: Q3476196
cites work: Comparisons of nonnegative splittings of matrices
cites work: Q3281387
cites work: Q5342712
cites work: Q5639278
OpenAlex ID: W1985064385
description: scientific article; zbMATH DE number 569156