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Convergence of the Cyclic Reduction Algorithm for a Class of Weakly Overdamped Quadratics

Convergence of the Cyclic Reduction Algorithm for a Class of Weakly Overdamped Quadratics
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Year:    2012

Journal of Computational Mathematics, Vol. 30 (2012), Iss. 2 : pp. 139–156

Abstract

In this paper, we establish a convergence result of the cyclic reduction (CR) algorithm for a class of weakly overdamped quadratic matrix polynomials without assumption that the partial multiplicities of the $n$th largest eigenvalue are all equal to 2. Our result can be regarded as a complement of that by Guo, Higham and Tisseur [SIAM J. Matrix Anal. Appl., 30 (2009), pp. 1593-1613]. The numerical example indicates that the convergence behavior of the CR algorithm is largely dictated by our theory.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1110-m3395

Journal of Computational Mathematics, Vol. 30 (2012), Iss. 2 : pp. 139–156

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Weakly overdamped quadratics Cyclic reduction Doubling algorithm.

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