On the monotonicity of incomplete factorization
type: Item
instance of: scholarly article
title: On the monotonicity of incomplete factorization
zbMATH Open document ID: 0682.65015
DOI: 10.1007/BF01386424
author: Tibor Fiala
published in: Numerische Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133462
review text: The Meijerink, van der Vorst type incomplete decomposition uses a position set, where the factors must be zero, but their product may differ from the original matrix. The smaller this position set is, the more the product of incomplete factors resembles the original matrix. The aim of this paper is to discuss this type of monotonicity. It is shown using the Perron Frobenius theory of nonnegative matrices, that the spectral radius of the iteration matrix is a monotone function of the position set. On the other hand no matrix norm of the iteration matrix depends monotonically on the position set. Comparison is made with the modified incomplete factorization technique.
reviewed by: T.Fiala
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 4117740
zbMATH Keywords: monotonicity
zbMATH Keywords: Perron Frobenius theory
zbMATH Keywords: nonnegative matrices
zbMATH Keywords: spectral radius
zbMATH Keywords: iteration matrix
zbMATH Keywords: incomplete factorization
zbMATH Keywords: M-matrices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4117740