文献类型：期刊文献

英文题名：Restarted generalized second-order krylov subspace methods for solving quadratic eigenvalue problems

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

机构：[1] Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, China; [2] Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China; [3] School of Mathematical Sciences, Fudan University, Shanghai 200433, China; [4] Key Laboratory of Mathematics for Nonlinear Sciences [Fudan University], China

年份：2010

卷号：4

期号：3

起止页码：148

外文期刊名：International Journal of Computational and Mathematical Sciences

收录：EI(收录号：20103413175258)

语种：英文

外文关键词：Degrees of freedom (mechanics) - Eigenvalues and eigenfunctions - Numerical methods - Vectors - Problem solving - Acoustic fields - Fluid mechanics

摘要：This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and present a generalized second-order Arnoldi process for constructing an orthonormal basis of the generalized second-order Krylov subspace. Then, by using the projection technique and the refined projection technique, we propose a restarted generalized second-order Arnoldi method and a restarted refined generalized second-order Arnoldi method for computing some eigenpairs of largescale quadratic eigenvalue problems. Some theoretical results are also presented. Some numerical examples are presented to illustrate the effectiveness of the proposed methods.