On the distance from a matrix polynomial to matrix polynomials with k prescribed distinct eigenvalues

被引：4

作者：

Kokabifar, E. ^{[1
]}

Loghmani, G. B. ^{[1
]}

Psarrakos, P. J. ^{[2
]}

Karbassi, S. M. ^{[3
]}

机构：

[1] Yazd Univ, Fac Sci, Dept Math, Yazd, Iran

[2] Natl Tech Univ Athens, Dept Math, Athens, Greece

[3] Islamic Azad Univ, Yazd Branch, Dept Math, Yazd, Iran

来源：

LINEAR & MULTILINEAR ALGEBRA | 2017年 / 65卷 / 04期

关键词：

Matrix polynomial; eigenvalue; perturbation; singular value; NEAREST MATRIX; SENSITIVITY;

D O I：

10.1080/03081087.2016.1202181

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider an n x n matrix polynomial P(lambda) and a set Sigma consisting of k <= n distinct complex numbers. In this paper, a (weighted) spectral norm distance from P(lambda) to the matrix polynomials whose spectra include the specified set Sigma, is defined and studied. An upper and a lower bound for this distance are obtained, and an optimal perturbation of P(lambda) associated to the upper bound is constructed. Numerical examples are given to illustrate the efficiency of the proposed bounds.

引用

页码：658 / 676

页数：19

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[2]

[Anonymous], 1997, Applied numerical linear algebra

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[Anonymous], 2002, NUMERICAL METHODS

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