Perturbation analysis for the eigenvalue problem of a formal product of matrices

被引：27

作者：

Benner, P

Mehrmann, V

Xu, HG

机构：

[1] Univ Bremen, Zentrum Technomath, Fachbereich Math & Informat 3, D-28334 Bremen, Germany

[2] Tech Univ Berlin, Fac Math & Nat Wissensch 2, D-10623 Berlin, Germany

[3] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

BIT NUMERICAL MATHEMATICS | 2002年 / 42卷 / 01期

关键词：

perturbation theory; eigenvalue problem; formal matrix products; periodic QZ algorithm; Hamiltonian matrix; skew-Hamiltonian matrix; deflating subspace;

D O I：

10.1023/A:1021966001542

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We study the perturbation theory for the eigenvalue problem of a formal matrix product A(1)(s1)...A(p)(s p), where all A(k) and square and s(k) is an element of {-1, 1}. We generalize the classical perturbation results for matrices and matrix pencils to perturbation results for generalized deflating subspaces and eigenvalues of such formal matrix products. As an application we then extend the structured perturbation theory for the eigenvalue problem of Hamiltonian matrices to Hamiltonian/skew-Hamiltonian pencils.

引用

页码：1 / 43

页数：43

共 36 条

[1] A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils [J].