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Nearness results for real tridiagonal 2‐Toeplitz matrices
Author(s) -
Bebiano Natália,
Furtado Susana
Publication year - 2019
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2257
Subject(s) - toeplitz matrix , tridiagonal matrix , mathematics , eigenvalues and eigenvectors , matrix norm , combinatorics , matrix (chemical analysis) , matrix analysis , dimension (graph theory) , pure mathematics , physics , quantum mechanics , materials science , composite material
Summary In this article, we extend the results for Toeplitz matrices obtained by Noschese, Pasquini, and Reichel. We study the distance d , measured in the Frobenius norm, of a real tridiagonal 2‐Toeplitz matrix T to the closureN T Rof the set formed by the real irreducible tridiagonal normal matrices. The matrices inN T R , whose distance to T is d , are characterized, and the location of their eigenvalues is shown to be in a region determined by the field of values of the operator associated with T , when T is in a certain class of matrices that contains the Toeplitz matrices. When T has an odd dimension, the eigenvalues of the closest matrices to T inN T Rare explicitly described. Finally, a measure of nonnormality of T is studied for a certain class of matrices T . The theoretical results are illustrated with examples. In addition, known results in the literature for the case in which T is a Toeplitz matrix are recovered.