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.
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.