三次特征值问题的迭代shift-and-invert Arnoldi算法（英文）  

An iterated shift-and-invert Arnoldi algorithm for cubic eigenvalue problems

作　　者：王正盛[1] 左钱 张敏[1] 慕黎明[1] 徐贵力[2] 

机构地区：[1]南京航空航天大学理学院,南京211106 [2]南京航空航天大学自动化学院,南京211106

出　　处：《应用数学与计算数学学报》2017年第2期213-223,共11页Communication on Applied Mathematics and Computation

基　　金：supported by the National Natural Science Foundation of China(61473148);the Natural Science Foundation of Jiangsu Province of China(BK20141408);Jiangsu Oversea Research and Training Program for University Prominent Young and Middle-aged Teachers and Presidents

摘　　要：对于求解大规模二次特征值问题,叶强提出了一种迭代shift-and-invert Arnoldi投影算法(Ye Q.An iterated shift-and-invert Arnoldi algorithm for quadratic matrix eigenvalue problems.Appl Math Compt,2006,172:818-827).将这一策略推广到求解大规模三次特征值问题,基于改进的Krylov子空间,给出了求解大规模三次特征值问题的一种迭代shiftand-invert Arnoldi算法.结果表明,结合shift-and-invert技术,这是一种具有快速收敛性的高效算法.数值试验结果验证了算法的有效性.To solve the large scale quadratic eigenvalue problem （QEP） L（λ）x ：= （λ2A ＋ λB ＋ C）x = 0, Ye proposed an iterated shift-and-invert Arnoldi projection algorithm based on the Krylov subspaces solely generated by the matrix A-1B （Ye Q. An iterated shift-and-invert Arnoldi algorithm for quadratic matrix eigenvalue problems. Appl Math Compt, 2006, 172： 818-827）. In this paper, we generalize this strategy for solving the large scale cubic eigenvalue problem （CEP）L（λ）x ：= （λ2A ＋ λB ＋ C）x = 0. Namely, we propose an extension of the iterated shift-and-invert Arnoldi algorithm from the QEP to the CEP. It is shown that, when iteratively combined with the shift-and-invert technique, it results in a fast converging algorithm for the CEP, which has the similar behavior of Ye＇s algorithm for the QEP. Numerical experiments are presented to illustrate this algorithm.

关 键 词：shift—and—invert ARNOLDI KRYLOV子空间 三次特征值问题 二次特征值问题 

分 类 号：O241.6[理学—计算数学]