The Bauer-Type Factorization of Matrix Polynomials Revisited and Extended

 
PIIS004446690000371-9-1
DOI10.31857/S004446690000371-9
Publication type Article
Status Published
Authors
Affiliation: University of Bergen
Address: Norway
Affiliation: Université de Brest
Address: France
Journal nameZhurnal vychislitelnoi matematiki i matematicheskoi fiziki
EditionVolume 58 Issue 7
Pages1073-1083
Abstract

For a Laurent polynomial a(λ), which is Hermitian and positive definite on the unit circle, the Bauer method provides the spectral factorization a(λ)=p(λ)p*(λ-1), where p(λ) is a polynomial having all its roots outside the unit circle. Namely, as the size of the banded Hermitian positive definite Toeplitz matrix associated with the Laurent polynomial increases, the coefficients at the bottom of its Cholesky lower triangular factor tend to the coefficients of p(λ). We study extensions of the Bauer method to the non-Hermitian matrix case. In the Hermitian case, we give new convergence bounds with computable coefficients.

KeywordsBauer-type method, spectral factorization, Wiener–Hopf factorization, banded Toeplitz matrix
Received10.10.2018
Publication date11.10.2018
Number of characters918
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