Overlapping additive and multiplicative Schwarz iterations for \(H\)-matrices
type: Item
instance of: scholarly article
title: Overlapping additive and multiplicative Schwarz iterations for \(H\)-matrices
zbMATH Open document ID: 1066.65036
author: R. Bru
author: Francisco Pedroche
author: Daniel B. Szyld
published in: Linear Algebra and its Applications
publication date: 2005-01-11T00:00:00Z
review text: A matrix \(A=(a_{ij})\) is called an \(H\)-matrix if the matrix with the diagonal entries \(| a_{ii}| \) and the off-diagonal entries \(\,-| a_{ij}| \) is a nonsingular \(M\)-matrix. These matrices were already considered by Ostrowski in 1937. In this paper, additive and multiplicative Schwarz methods are considered for linear systems with \(H\)-matrices, and results on \(M\)-matrices or symmetric positive definite matrices are extended to them. The case of inexact local solvers is also considered. Note that \(A\) is an \(H\)-matrix iff there is a nonsingular diagonal matrix \(U\) such that \(U^{-1}AU\) is diagonally dominant. The matrix \(U\) corresponds to a rescaling, and Schwarz iterations are invariant under scaling transformations.
reviewed by: D. Braess
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 2126344
zbMATH Keywords: H-matrices
zbMATH Keywords: Schwarz iterative methods
zbMATH Keywords: Block methods
zbMATH Keywords: Overlap
zbMATH Keywords: M-matrices
zbMATH Keywords: additive and multiplicative Schwarz methods
zbMATH Keywords: diagonally dominant
zbMATH Keywords: scaling transformations
MaRDI profile type: Publication
full work available at URL: j.laa.2003.10.022
OpenAlex ID: W2027158013
Wikidata QID: Q115156461
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DOI: 10.1016/J.LAA.2003.10.022
description: scientific article; zbMATH DE number 2126344