Matrix polynomials with specified eigenvalues

被引：4

作者：

Karow, Michael ^{[1
]}

Mengi, Emre ^{[2
]}

机构：

[1] TU Berlin, Dept Math, D-10623 Berlin, Germany

[2] Koc Univ, Dept Math, TR-34450 Istanbul, Turkey

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 466卷

关键词：

Matrix polynomial; Linearization; Singular values; Sylvester equation; Eigenvalue perturbation theory; MULTIPLE-EIGENVALUES; CRITICAL-POINTS; PSEUDOSPECTRA; DISTANCE; FORMULA;

D O I：

10.1016/j.laa.2014.10.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work concerns the distance in the 2-norm from a given matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Initially, we consider perturbations of the constant coefficient matrix only. A singular value optimization characterization is derived for the associated distance. We also consider the distance in the general setting, when all of the coefficient matrices are perturbed. In this general setting, we obtain a lower bound in terms of another singular value optimization problem. The singular value optimization problems derived facilitate the numerical computation of the distances. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：457 / 482

页数：26

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