文献类型：期刊文献

英文题名：Restarted generalized Krylov subspace methods for solving large-scale polynomial eigenvalue problems

作者：Bao, Liang[1];Lin, Yiqin[2];Wei, Yimin[3,4]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Hunan Univ Sci & Engn, Dept Math & Computat Sci, Yongzhou 425006, Peoples R China;[3]Fudan Univ, Sch Math Sci, Inst Math, Shanghai 200433, Peoples R China;[4]Fudan Univ, Minist Educ, Key Lab Math Nonlinear Sci, Beijing, Peoples R China

年份：2009

卷号：50

期号：1

起止页码：17

外文期刊名：NUMERICAL ALGORITHMS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000263899000002)】；

基金：Yiqin Lin is supported by Scientific Research Startup Foundation of Hunan University of Science and Engineering.Yimin Wei is supported by the National Natural Science Foundation of China and Shanghai Education Committee.

语种：英文

外文关键词：Polynomial eigenvalue problem; Generalized Krylov subspace; Generalized Arnoldi procedure; Projection technique; Refined technique; Restarting

摘要：In this paper, we introduce a generalized Krylov subspace G(m)(A;u) based on a square matrix sequence {A(j)} and a vector sequence {u(j)}. Next we present a generalized Arnoldi procedure for generating an orthonormal basis of G(m)(A;u). By applying the projection and the refined technique, we derive a restarted generalized Arnoldi method and a restarted refined generalized Arnoldi method for solving a large-scale polynomial eigenvalue problem (PEP). These two methods are applied to solve the PEP directly. Hence they preserve essential structures and properties of the PEP. Furthermore, restarting reduces the storage requirements. Some theoretical results are presented. Numerical tests report the effectiveness of these methods.