Block Toeplitz matrices and preconditioning
type: Item
instance of: scholarly article
title: Block Toeplitz matrices and preconditioning
zbMATH Open document ID: 0934.65038
DOI: 10.1007/BF02575709
author: S. H. Smith
published in: Calcolo
publication date: 1998-08-10T00:00:00Z
review text: The authors investigate the asymptotic behaviour of the eigenvalues of Hermitian \(n\times n\) block Toeplitz matrices \(T_n\) with \(k\times k\) blocks, as \(n\to\infty\). They show that the spectrum of \(P^{-1}_nT_n\), where \(P_n\) is a given preconditioner, is contained in a certain interval. The limit values for both the condition numbers and the conjugate gradient convergence factor for matrices \(P^{-1}_nT_n\) are computed.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1186661
zbMATH Keywords: preconditioning
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: block Toeplitz matrices
zbMATH Keywords: condition numbers
zbMATH Keywords: convergence factor
reviewed by: Aurél Galántai
MaRDI profile type: Publication
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cites work: Conjugate Gradient Methods for Toeplitz Systems
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cites work: On the asymptotic spectrum of Hermitian block Toeplitz matrices with Toeplitz blocks
cites work: Asymptotic Spectra of Hermitian Block Toeplitz Matrices and Preconditioning Results
cites work: A unifying approach to some old and new theorems on distribution and clustering
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description: scientific article; zbMATH DE number 1186661