標題: A semiorthogonal generalized Arnoldi method and its variations for quadratic eigenvalue problems
作者: Huang, Wei-Qiang
Li, Tiexiang
Li, Yung-Ta
Lin, Wen-Wei
應用數學系
Department of Applied Mathematics
關鍵字: quadratic eigenvalue problem;semiorthogonal generalized Arnoldi method;orthogonal projection;refinement;refined shifts;implicit restart
公開日期: 1-三月-2013
摘要: In this paper, we are concerned with the computation of a few eigenpairs with smallest eigenvalues in absolute value of quadratic eigenvalue problems. We first develop a semiorthogonal generalized Arnoldi method where the name comes from the application of a pseudo inner product in the construction of a generalized Arnoldi reduction for a generalized eigenvalue problem. The method applies the RayleighRitz orthogonal projection technique on the quadratic eigenvalue problem. Consequently, it preserves the spectral properties of the original quadratic eigenvalue problem. Furthermore, we propose a refinement scheme to improve the accuracy of the Ritz vectors for the quadratic eigenvalue problem. Given shifts, we also show how to restart the method by implicitly updating the starting vector and constructing better projection subspace. We combine the ideas of the refinement and the restart by selecting shifts upon the information of refined Ritz vectors. Finally, an implicitly restarted refined semiorthogonal generalized Arnoldi method is developed. Numerical examples demonstrate that the implicitly restarted semiorthogonal generalized Arnoldi method with or without refinement has superior convergence behaviors than the implicitly restarted Arnoldi method applied to the linearized quadratic eigenvalue problem. Copyright (c) 2012 John Wiley & Sons, Ltd.
URI: http://dx.doi.org/10.1002/nla.1840
http://hdl.handle.net/11536/21189
ISSN: 1070-5325
DOI: 10.1002/nla.1840
期刊: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Volume: 20
Issue: 2
起始頁: 259
結束頁: 280
顯示於類別:期刊論文


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