Nearness results for real tridiagonal 2-Toeplitz matrices

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Bebiano, N (Author) Other; Susana Borges Furtado (Author) FEP

Journal

Title: Numerical Linear Algebra with Applications

Serial No. 2257 Vol. 26 No. Ed. 5

Pages: 1-17

ISSN: 1070-5325

Publisher: Wiley-Blackwell

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00Q-RHW

DOI: 10.1002/nla.2257

Abstract (EN): 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 closure NTR of the set formed by the real irreducible tridiagonal normal matrices. The matrices in NTR, 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 in NTR are 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17