Block second-order Krylov subspace methods for large-scale quadratic eigenvalue problems

Yiqin Lin

doi:10.1016/j.amc.2005.12.054

2006-10-01

PRE

Yiqin Lin *

Liang Bao

DOI：10.1016/j.amc.2005.12.054

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摘要

En 中文

In this paper, we first introduce a block second-order Krylov subspace G(m1),, (A, B; Q(1)) based on a pair of square matrices A and B and an orthonormal matrix Q(1). Then we present a block second-order Arnoldi procedure for generating an orthonormal basis of G(m1) (A, B; Q(1)) and a block second-order biorthogonalization procedure for generating biorthonormal basis of G(m1) (A, B; Q(1)) and G(m1) (A(T), B-T; P-1). By applying the projection techniques, we derive two block second-order Krylov subspace methods for solving a large-scale quadratic eigenvalue problem (QEP). These methods are applied to the QEP directly. Hence they preserve essential structures and properties of the QEP. Some theoretical results are given. Numerical experiments report the effectiveness of these methods. (c) 2006 Elsevier Inc. All rights reserved.

Keyword:

quadratic eigenvalue problem

block second-order Krylov subspace

block second-order Arnoldi procedure

block second-order biorthogonalization procedure