On five-diagonal Toeplitz matrices and orthogonal polynomials on the unit circle

DOI10.1007/BF02198300zbMath0838.42008OpenAlexW2033160393MaRDI QIDQ1895986

María Pilar Alfaro, Jesús María Montaner

Publication date: 17 September 1995

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02198300

zbMATH Keywords

orthogonal polynomialsquasi-definite moment functionalsband Toeplitz matricespositive-definitenessfive-diagonal Toeplitz matricesLebesgue moment functional

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (11)

A note on computing the inverse and the determinant of a pentadiagonal Toeplitz matrix ⋮ The use of the factorization of five-diagonal matrices by tridiagonal Toeplitz matrices ⋮ Properties of a class of perturbed Toeplitz periodic tridiagonal matrices ⋮ An explicit formula for the smoother weights of the Hodrick-Prescott filter ⋮ On the determinant evaluation of quasi penta-diagonal matrices and quasi penta-diagonal Toeplitz matrices ⋮ A symbolic algorithm for periodic tridiagonal systems of equations ⋮ An explicit formula for the inverse of a pentadiagonal Toeplitz matrix ⋮ The determinants of certain \((0,1)\) Toeplitz matrices ⋮ Numerical algorithm for the determinant evaluation of cyclic pentadiagonal matrices with Toeplitz structure ⋮ On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices ⋮ Some determinantal considerations for pentadiagonal matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Systems of orthogonal polynomials explicitly represented by Jacobi polynomials
• Determinant of block-Toeplitz band matrices
• Relation between polynomials orthogonal on the unit circle with respect to different weights
• On sieved orthogonal polynomials. IX: Orthogonality on the unit circle
• Classification problems in differential topology. VI: Classification of \((s-1)\)-connected \((2s+1)\)-manifolds
• Orthogonal polynomials on the unit circle: Symmetrization and quadratic decomposition
• On some problems connected with polynomials orthogonal on the complex unit circle
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
• Five-Diagonal Toeplitz Determinants an Their Relation to Chebyshev Polynomials
• Toeplitz Matrices Generated by the Laurent Series Expansion of an Arbitrary Rational Function

This page was built for publication: On five-diagonal Toeplitz matrices and orthogonal polynomials on the unit circle