Volume 30, Issue 2
Convergence of the Cyclic Reduction Algorithm for a Class of Weakly Overdamped Quadratics

J. Comp. Math., 30 (2012), pp. 139-156.

Published online: 2012-04

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• 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.

• Keywords

Weakly overdamped quadratics, Cyclic reduction, Doubling algorithm.

• AMS Subject Headings

15A24, 15A48.

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@Article{JCM-30-139, author = {}, title = {Convergence of the Cyclic Reduction Algorithm for a Class of Weakly Overdamped Quadratics}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {2}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1110-m3395}, url = {http://global-sci.org/intro/article_detail/jcm/8422.html} }
TY - JOUR T1 - Convergence of the Cyclic Reduction Algorithm for a Class of Weakly Overdamped Quadratics JO - Journal of Computational Mathematics VL - 2 SP - 139 EP - 156 PY - 2012 DA - 2012/04 SN - 30 DO - http://doi.org/10.4208/jcm.1110-m3395 UR - https://global-sci.org/intro/article_detail/jcm/8422.html KW - Weakly overdamped quadratics, Cyclic reduction, Doubling algorithm. AB -

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.

Bo Yu, Donghui Li & Ning Dong. (1970). Convergence of the Cyclic Reduction Algorithm for a Class of Weakly Overdamped Quadratics. Journal of Computational Mathematics. 30 (2). 139-156. doi:10.4208/jcm.1110-m3395
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