The Bauer-type factorization of matrix polynomials revisited and extended
type: Item
instance of: scholarly article
title: The Bauer-type factorization of matrix polynomials revisited and extended
zbMATH Open document ID: 1404.15010
DOI: 10.1134/S0965542518070126
author: A. Malyshev
author: M. Sadkane
published in: Computational Mathematics and Mathematical Physics
publication date: 2018-10-30T00:00:00Z
review text: A matrix Laurent polynomial \( A(\lambda) = A_1\lambda + A_0 + A_{-1}\lambda^{-1}\) where \(A_1, A_0, A_{-1}\in\mathbb{C}^{m\times m}\) is called nonsingular if the polynomial \(\text{det}(\lambda A(\lambda))\) does not identically vanish. The authors consider only Laurent polynomials that admit a factorization \( A(\lambda) = (X\lambda + I)S(I +Y\lambda^{-1})\). The authors obtain formulas for the factors in the LDU factorization of the Toeplitz matrix associated with Laurent polynomials. They obtain convergence estimates for the Brauer-type factorization. They give a convergence analysis for a matrix Laurent polynomial which is Hermitian and positive semidefinite on the unit circle. They give applications to Brauer's method for the Laurent polynomials of high degree.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15B05
zbMATH DE Number: 6968557
zbMATH Keywords: Bauer-type method
zbMATH Keywords: spectral factorization
zbMATH Keywords: Wiener-Hopf factorization
zbMATH Keywords: banded Toeplitz matrix
MaRDI profile type: Publication
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full work available at URL: s0965542518070126
OpenAlex ID: W2888528822
description: scientific article; zbMATH DE number 6968557