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

Bo Yu, Donghui Li & Ning Dong

DOI: 10.4208/jcm.1110-m3395

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

Published online: 2012-04

[An open-access article; the PDF is free to any online user.]

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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.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-139, author = {Bo Yu, Donghui Li and Ning Dong}, 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 AU - Bo Yu, Donghui Li & Ning Dong 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 and Ning Dong. (2012). 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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