A note on comparison theorems for nonnegative matrices
type: Item
instance of: scholarly article
title: A note on comparison theorems for nonnegative matrices
zbMATH Open document ID: 0557.65020
DOI: 10.1007/BF01389590
author: Valerie A. Miller
author: M. Neumann
published in: Numerische Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133044
review text: In a recent paper, \textit{G. Csordas} and \textit{R. S. Varga} [Comparisons of regular splittings and matrices, ibid. 44, 23-25 (1984)] unified and extended earlier theorems of \textit{R. S. Varga} [Boundary Probl. in diff. Equations, Proc. Sympos., Madison, April 20-22, 1959, 121-142 (1960; Zbl 0100.125)] and \textit{Z. Woźnicki} [Two-sweep iterative methods for solving large linear systems and their application to the numerical solution of multi-group multi-dimensional neutron diffusion equation, Diss., Inst. Nucl. Research, Swicrk/Otwocka, Poland (1973)] on the comparison of the asymptotic rates of convergence of two iteration matrices induced by two regular splittings. The main purpose of this note is to show a connection between the Csordas-Varga paper and a paper by \textit{R. Beauwens} [Numer. Math. 31, 335-357 (1979; Zbl 0431.65012)], in which a comparison theorem is developed for the asymptotic rate of convergence of two nonnegative iteration matrices induced by two splittings which are not necessarily regular. Monotonic norms already used in Beauwens play an important role in our work here.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 3888800
zbMATH Keywords: comparison
zbMATH Keywords: asymptotic rates of convergence
zbMATH Keywords: regular splittings
zbMATH Keywords: nonnegative iteration matrices
zbMATH Keywords: monotonic norms
MaRDI profile type: Publication
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OpenAlex ID: W2060249776
description: scientific article; zbMATH DE number 3888800