On the construction of Szegő polynomials

DOI10.1016/0377-0427(93)90299-QzbMath0819.65012OpenAlexW1607484412MaRDI QIDQ1802171

Carl Jagels, Lothar Reichel

Publication date: 11 August 1993

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(93)90299-q

zbMATH Keywords

momentsorthogonal polynomialsSzegő polynomialsconditioningSchur's algorithmrecursion coefficientsChebyshev procedureStieltjes procedures

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Computation of special functions and constants, construction of tables (65D20)

Related Items (7)

Sensitivity analysis for Szegő polynomials ⋮ Trigonometric orthogonal systems and quadrature formulae ⋮ Szegő-Lobatto quadrature rules ⋮ Modified Chebyshev algorithm: some applications ⋮ On an Economic Arnoldi Method for $BML$-Matrices ⋮ Generalized averaged Szegő quadrature rules ⋮ Continuation methods for the computation of zeros of Szegő polynomials

Uses Software

• EISPACK
• UDC

Cites Work

• A divide and conquer method for unitary and orthogonal eigenproblems
• Orthogonal polynomials - Constructive theory and applications
• The QR algorithm for unitary Hessenberg matrices
• Extensions of Szegö's theory of orthogonal polynomials. III
• Downdating of Szegö polynomials and data-fitting applications
• Characterization of measures associated with orthogonal polynomials on the unit circle
• Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
• On the sensitivity of orthogonal polynomials to perturbations in the moments
• Matrix eigensystem routines - EISPACK guide
• A class of orthogonal polynomials
• Szegö polynomials associated with Wiener-Levinson filters
• On the distribution of zeros of polynomials orthogonal on the unit circle
• Fast Approximation of Dominant Harmonics
• Discrete Least Squares Approximation by Trigonometric Polynomials
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
• The Numerical Stability of the Levinson-Durbin Algorithm for Toeplitz Systems of Equations
• On Generating Orthogonal Polynomials
• An implementation of a divide and conquer algorithm for the unitary eigen problem
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the construction of Szegő polynomials