A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems

被引：26

作者：

Li, RC ^{[1
]}

Ye, Q ^{[1
]}

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2003年 / 25卷 / 02期

关键词：

quadratic matrix polynomial; Krylov subspace; quadratic eigenvalue problem; least squares problem; quadratic constraint;

D O I：

10.1137/S0895479802409390

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a Krylov subspace-type projection method for a quadratic matrix polynomial lambda(2)I - lambdaA - B that works directly with A and B without going through any linearization. We discuss a special case when one matrix is a low rank perturbation of the other matrix. We also apply the method to solve quadratically constrained linear least squares problem through a reformulation of Gander, Golub, and von Matt as a quadratic eigenvalue problem, and we demonstrate the effectiveness of this approach. Numerical examples are given to illustrate the efficiency of the algorithms.

引用

页码：405 / 428

页数：24

共 33 条

[1]

[Anonymous], 1997, ARPACK Users' Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods, DOI 10.1137/1.9780898719628

[2] THE PRINCIPLE OF MINIMIZED ITERATIONS IN THE SOLUTION OF THE MATRIX EIGENVALUE PROBLEM [J].