The Bauer-Type Factorization of Matrix Polynomials Revisited and Extended

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.

Keywords

Bauer-type method, spectral factorization, Wiener–Hopf factorization, banded Toeplitz matrix

Received

10.10.2018

Publication date

11.10.2018

Number of characters

918

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GOST	Malyshev A., Sadkane M. The Bauer-Type Factorization of Matrix Polynomials Revisited and Extended // Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki – 2018. – V. 58. – Issue 7 C. 1073-1083 [Electronic resource]. URL: http://ras.jes.su/zvmmf/s004446690000371-9-1-en (circulation date: 27.04.2024). DOI: 10.31857/S004446690000371-9
MLA	Malyshev, A., Sadkane, M. "The Bauer-Type Factorization of Matrix Polynomials Revisited and Extended." Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki 58.7 (2018):1073-1083. DOI: 10.31857/S004446690000371-9
APA	Malyshev A., Sadkane M. (2018). The Bauer-Type Factorization of Matrix Polynomials Revisited and Extended. Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki 58(7), pp.1073-1083 DOI: 10.31857/S004446690000371-9

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