The computation of the square roots of circulant matrices
type: Item
instance of: scholarly article
title: The computation of the square roots of circulant matrices
zbMATH Open document ID: 1229.65068
author: Chengbo Lu
author: Chuanqing Gu
published in: Applied Mathematics and Computation
publication date: 2011-04-19T00:00:00Z
review text: The authors construct the reduced forms of circulant matrices and quasi-skew circulant matrices. Then they show that the problem of computing the circulant square roots of a circulant matrix \(A\) can be reduced to that of computing the square roots of two half size matrices \(B-C\) and \(B+C\). Two efficient algorithms are presented to compute their square roots. Those methods are faster than the traditional algorithm which is based on the Schur decomposition. They further consider circulant \(H\)-matrices with positive diagonal entries and develop two algorithms for computing their principal square roots. Those two algorithms are based on \(LL\) iteration and the modified Schulz iterative method, respectively. Some numerical experiments are presented.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 5880120
zbMATH Keywords: circulant matrix
zbMATH Keywords: quasi-skew circulant matrix
zbMATH Keywords: principal square root
zbMATH Keywords: reduced form
zbMATH Keywords: \(H\)-matrix
zbMATH Keywords: \(M\)-matrix
zbMATH Keywords: Schur decomposition
zbMATH Keywords: algorithms
zbMATH Keywords: numerical experiments
describes a project that uses: testmatrix
describes a project that uses: mctoolbox
describes a project that uses: mftoolbox
MaRDI profile type: Publication
full work available at URL: j.amc.2011.01.018
OpenAlex ID: W2031086457
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DOI: 10.1016/J.AMC.2011.01.018
description: scientific article; zbMATH DE number 5880120