Rational Gauss-Chebyshev quadrature formulas for complex poles outside $[-1,1]$

DOI10.1090/S0025-5718-07-01982-5zbMath1136.42304OpenAlexW1989750786MaRDI QIDQ5444313

Karl Deckers, Joris Van Deun, Adhemar Bultheel

Publication date: 25 February 2008

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01982-5

zbMATH Keywords

quadrature formulasorthogonal rational functions

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Numerical quadrature and cubature formulas (65D32)

Related Items (14)

CHRISTOFFEL FUNCTIONS AND UNIVERSALITY LIMITS FOR ORTHOGONAL RATIONAL FUNCTIONS ⋮ A numerical solution of the constrained weighted energy problem ⋮ Computing near-best fixed pole rational interpolants ⋮ Positive rational interpolatory quadrature formulas on the unit circle and the interval ⋮ A generalized eigenvalue problem for quasi-orthogonal rational functions ⋮ Chebyshev series method for computing weighted quadrature formulas ⋮ An extension of the associated rational functions on the unit circle ⋮ The existence and construction of rational Gauss-type quadrature rules ⋮ Eigenvalue problems to compute almost optimal points for rational interpolation with prescribed poles ⋮ Rational interpolation. II: Quadrature and convergence ⋮ Rational Szegő quadratures associated with Chebyshev weight functions ⋮ An extended relation between orthogonal rational functions on the unit circle and the interval \([ - 1,1\)] ⋮ Cubature rules for unitary Jacobi ensembles ⋮ Computing rational Gauss-Chebyshev quadrature formulas with complex poles: The algorithm

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• Boundary asymptotics for orthogonal rational functions on the unit circle
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• Szegö quadrature formulas for certain Jacobi-type weight functions
• EQUILIBRIUM MEASURE AND THE DISTRIBUTION OF ZEROS OF EXTREMAL POLYNOMIALS
• Quadrature Formulas Based on Rational Interpolation
• On computing rational Gauss-Chebyshev quadrature formulas

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