Nearness results for real tridiagonal 2‐Toeplitz matrices
Natália Bebiano, Susana Furtado · Numerical Linear Algebra with Applications · 2019
Summary In this article, we extend the results for Toeplitz matrices obtained by Noschese, Pasquini, and Reichel. We study the distanced, measured in the Frobenius norm, of a real tridiagonal 2‐Toeplitz matrixTto the closure of the set formed by the real irreducible tridiagonal normal matrices. The matrices in , whose distance toTisd, 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 withT, whenTis in a certain class of matrices that contains the Toeplitz matrices. WhenThas an odd dimension, the eigenvalues of the closest matrices toTin are explicitly described. Finally, a measure of nonnormality ofTis studied for a certain class of matricesT. The theoretical results are illustrated with examples. In addition, known results in the literature for the case in whichTis a Toeplitz matrix are recovered.