On five-diagonal Toeplitz matrices and orthogonal polynomials on the unit circle
type: Item
instance of: scholarly article
title: On five-diagonal Toeplitz matrices and orthogonal polynomials on the unit circle
zbMATH Open document ID: 0838.42008
DOI: 10.1007/BF02198300
published in: Numerical Algorithms
publication date: 1995-09-17T00:00:00Z
review text: This paper deals with modifications of the Lebesgue moment functional on the unit circle by trigonometric polynomials of degree 2. The associated Toeplitz matrix is five-diagonal. The authors study the quasi-definiteness and the positive-definiteness of the corresponding moment functional. Further, they use the factorization of a five-diagonal matrix as a product of two tridiagonal matrices [see \textit{R. B. Marr} and \textit{G. H. Vineyard}, SIAM J. Matrix Anal. Appl. 9, No. 4, 579-586 (1988; Zbl 0661.15006)]\ to study the existence of the orthogonal polynomials.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 784685
zbMATH Keywords: five-diagonal Toeplitz matrices
zbMATH Keywords: band Toeplitz matrices
zbMATH Keywords: quasi-definite moment functionals
zbMATH Keywords: Lebesgue moment functional
zbMATH Keywords: positive-definiteness
zbMATH Keywords: orthogonal polynomials
author: Jesús María Montaner
author: María Pilar Alfaro
reviewed by: Roelof Koekoek
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02198300
OpenAlex ID: W2033160393
description: scientific article; zbMATH DE number 784685