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

被引:3
作者
Kokabifar, E. [1 ]
Psarrakos, P. J. [2 ]
Loghmani, G. B. [1 ]
机构
[1] Yazd Univ, Fac Sci, Dept Math, Yazd, Iran
[2] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece
基金
美国国家科学基金会;
关键词
Matrix polynomial; Eigenvalue; Perturbation; Singular value; Jordan chain; ILL-CONDITIONED EIGENPROBLEM; NEAREST MATRIX; SENSITIVITY;
D O I
10.1016/j.laa.2018.01.010
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Consider an n x n matrix polynomial P(lambda) and a set Sigma consisting of k <= n complex numbers. Recently, Kokabifar, Loghmani, Psarrakos and Karbassi studied a (weighted) spectral norm distance from P(lambda) to the n x n matrix polynomials whose spectra contain the specified set Sigma, under the assumption that all the entries of Sigma are distinct. In this paper, the case in which some or all of the desired eigenvalues can be multiple is discussed. Lower and upper bounds for the distance are computed, and a perturbation of P(lambda) associated to the upper bound is constructed. A detailed numerical example illustrates the efficiency and validity of the proposed computational method. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码:158 / 185
页数:28
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