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The inverse of nonsymmetric two-level Toeplitz operator matrices
Journal article   Open access   Peer reviewed

The inverse of nonsymmetric two-level Toeplitz operator matrices

Selcuk Koyuncu and Hugo J. Woerdeman
Linear algebra and its applications, v 437(9), pp 2142-2158
01 Nov 2012
DOI: https://doi.org/10.1016/j.laa.2012.04.048
url
https://doi.org/10.1016/j.laa.2012.04.048View
Published, Version of Record (VoR)Open Access (Publisher-Specific),  Open

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
The Gohberg-Semencul formula allows one to express the entries of the inverse of a Toeplitz matrix using only a few entries (the first row and the first column) of the inverse matrix, under some nonsingularity condition. In this paper we will provide a two variable generalization of the Gohberg-Semencul formula in the case of a nonsymmetric two-level Toeplitz matrix with a symbol of the form f(z(1),z(2)) = 1/<(P(Z(1),Z(2)) )over bar> Q(Z(1),Z(2)) where P(Z(1),Z(2)) and Q(Z(1),Z(2)) are stable polynomials of two variables. We also consider the case of operator valued two-level Toeplitz matrices. In addition, we propose an equation solver involving two-level Toeplitz matrices. Numerical results are included. (C) 2012 Elsevier Inc. All rights reserved.

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Mathematics
Mathematics, Applied
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