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 - <p style="text-align: justify;">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.</p>