Generalizations of the projection method with applications to SOR theory for Hermitian positive semidefinite linear systems
type: Item
instance of: scholarly article
title: Generalizations of the projection method with applications to SOR theory for Hermitian positive semidefinite linear systems
zbMATH Open document ID: 0628.65024
DOI: 10.1007/BF01396746
author: Stuart Nelson
author: M. Neumann
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133188
review text: Eine quadratische Matrix B heißt parakontrahierend, falls \(\| B\|_ 2\leq 1\) und \(\| Bx\|_ 2<\| x\|_ 2\) für alle \(x\in 0\) mit \(x\in [N(I-B)]^{\perp}\), wobei N der Kern von I-B ist. Es wird gezeigt, daß ein Produkt parakontrahierender Matrizen, wieder parakontrahierend ist. Der Betrag des subdominanten Eigenwerts des Produkts wird abgeschätzt. Das Ergebnis wird auf das SOR-Verfahren zur Lösung von \(Ax=b\) in dem Fall angewandt, daß A Hermitesch und positiv semidefinit ist.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4022474
zbMATH Keywords: projection method
zbMATH Keywords: Hermitian positive semidefinite linear systems
zbMATH Keywords: paracontracting matrices
zbMATH Keywords: subdominant eigenvalue
zbMATH Keywords: SOR iteration matrix
zbMATH Keywords: successive overrelaxation
MaRDI profile type: Publication
cites work: Q3943082
cites work: Numerical Methods for Computing Angles Between Linear Subspaces
cites work: Nested bounds for the Perron root of a nonnegative matrix
cites work: Q3694559
cites work: On the von Neumann alternating algorithm in Hilbert space
cites work: Q5518786
cites work: On the Solution of Singular and Semidefinite Linear Systems by Iteration
cites work: Matrix algebras and groups relatively bounded in norm
cites work: Q3254702
cites work: Upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices
cites work: Non-negative matrices and Markov chains. 2nd ed
cites work: Practical and mathematical aspects of the problem of reconstructing objects from radiographs
cites work: Positive-definite matrices and their role in the study of the characteristic roots of general matrices
cites work: Q5342712
cites work: On Weakly Positive Matrices
cites work: Q5639278
OpenAlex ID: W2039577138
description: scientific article; zbMATH DE number 4022474