Szegő-Lobatto quadrature rules

DOI10.1016/j.cam.2005.12.009zbMath1109.65027OpenAlexW2074694609MaRDI QIDQ859867

Carl Jagels, Lothar Reichel

Publication date: 22 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.cam.2005.12.009

zbMATH Keywords

eigenvalue problemtrigonometric polynomialsupper Hessenberg matrixintegration of periodic functionsSzegö polynomialSzegö quadrature ruleSzegö-Lobatto quadrature rule

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (17)

Sieved para-orthogonal polynomials on the unit circle ⋮ Sensitivity analysis for Szegő polynomials ⋮ On Gauss-type quadrature formulas with prescribed nodes anywhere on the real line ⋮ Trigonometric orthogonal systems and quadrature formulae ⋮ Computation of rational Szegő-Lobatto quadrature formulas ⋮ Positive rational interpolatory quadrature formulas on the unit circle and the interval ⋮ On bi-orthogonal systems of trigonometric functions and quadrature formulas for periodic integrands ⋮ Szegő-type quadrature formulas ⋮ Quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity ⋮ Stieltjes-type polynomials on the unit circle ⋮ Rational Szegő quadratures associated with Chebyshev weight functions ⋮ Generalized averaged Szegő quadrature rules ⋮ Optimally Conditioned Vandermonde-Like Matrices ⋮ Zeros of quasi-paraorthogonal polynomials and positive quadrature ⋮ Orthogonal Laurent polynomials on the unit circle and snake-shaped matrix factorizations ⋮ A connection between Szegő-Lobatto and quasi Gauss-type quadrature formulas ⋮ Error estimates for some quadrature rules with maximal trigonometric degree of exactness

Uses Software

• UNCMND
• GAUSSIAN
• pchip
• OPQ
• UDC

Cites Work

• A divide and conquer method for unitary and orthogonal eigenproblems
• The QR algorithm for unitary Hessenberg matrices
• Downdating of Szegö polynomials and data-fitting applications
• Gaussian quadrature formulae on the unit circle
• The interplay between classical analysis and (numerical) linear algebra -- a tribute to Gene H. Golub
• Positive interpolatory quadrature formulas and para-orthogonal polynomials
• Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
• On the construction of Szegő polynomials
• Orthogonal Laurent polynomials and quadratures on the unit circle and the real half-line
• Anti-Szego quadrature rules
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
• An implementation of a divide and conquer algorithm for the unitary eigen problem
• A Stable Divide and Conquer Algorithm for the Unitary Eigenproblem
• An Error Analysis of a Unitary Hessenberg QR Algorithm
• A connection between quadrature formulas on the unit circle and the interval \([-1,1\)]
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