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Alimohammad Nazari

Alimohammad Nazari

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-3231-0340
Education: PhD.
ScopusId: 7003903991
HIndex:
Faculty: Science
Address: Arak University
Phone:

Research

Title
On the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues
Type
JournalPaper
Keywords
Matrix polynomial, Eigenvalue, Perturbation, Singular value,
Year
2015
Journal Wavelets and Linear Algebra
DOI
Researchers Esmail kokabifar ، barid loghmani ، Alimohammad Nazari ، seyyed mohammadreza karbasi

Abstract

Consider an nn matrix polynomial P(). A spectral norm distance from P() to the set of n  n matrix polynomials that have a given scalar  2 C as a multiple eigenvalue was introduced and obtained by Papathanasiou and Psarrakos. They computed lower and upper bounds for this distance, constructing an associated perturbation of P(). In this paper, we extend this result to the case of two given distinct complex numbers 1 and 2. First, we compute a lower bound for the spectral norm distance from P() to the set of matrix polynomials that have 1; 2 as two eigenvalues. Then we construct an associated perturbation of P() such that the perturbed matrix polynomial has two given scalars 1 and 2 in its spectrum. Finally, we derive an upper bound for the distance by the constructed perturbation of P(). Numerical examples are provided to illustrate the validity of the method. c⃝