Matrix compensation and diagonal compensation
type: Item
instance of: scholarly article
title: Matrix compensation and diagonal compensation
zbMATH Open document ID: 0857.65051
DOI: 10.1016/0377-0427(95)00077-1
published in: Journal of Computational and Applied Mathematics
publication date: 1997-03-09T00:00:00Z
review text: Let \(A\) be a symmetric positive definite matrix which is decomposed as \(A=B+R\) in some natural way. Typically \(B\) has a special sparsity pattern and \(R\) can be considered as a ``rest''. A matrix \(D\) is called a compensative matrix of \(R\) if \(D-R\) is positive semidefinite. Now define \(M=B+D\), so \(M\) is a compensative matrix of \(A\). \(M\) can be an efficient preconditioner of \(A\). In the paper diagonal compensation is generalized to positive definite matrices. The aim is to preserve the positivity of matrices. Several results are proved on the condition of the preconditioned matrices but no numerical examples are given.
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 903503
zbMATH Keywords: positive matrix
zbMATH Keywords: symmetric positive definite matrix
zbMATH Keywords: compensative matrix
zbMATH Keywords: preconditioner
zbMATH Keywords: diagonal compensation
author: Lu, Hao
reviewed by: Willy J. F. Govaerts
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00077-1
OpenAlex ID: W2169778792
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description: scientific article; zbMATH DE number 903503