Recurrence and asymptotics for orthonormal rational functions on an interval

DOI10.1093/imanum/drm048zbMath1159.65025OpenAlexW2032458116MaRDI QIDQ3600853

Karl Deckers, Adhemar Bultheel

Publication date: 6 February 2009

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.cs.kuleuven.be/cwis/research/nalag/papers/ade/orfas/

zbMATH Keywords

convergenceasymptoticsorthogonal rational functionsthree-term recurrence relationcomplex poles

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Computation of special functions and constants, construction of tables (65D20) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Other special orthogonal polynomials and functions (33C47) Numerical approximation and evaluation of special functions (33F05)

Related Items (11)

CHRISTOFFEL FUNCTIONS AND UNIVERSALITY LIMITS FOR ORTHOGONAL RATIONAL FUNCTIONS ⋮ Orthogonal rational functions on the extended real line and analytic on the upper half plane ⋮ Positive rational interpolatory quadrature formulas on the unit circle and the interval ⋮ Rational Gauss quadrature rules for the approximation of matrix functionals involving Stieltjes functions ⋮ A generalized eigenvalue problem for quasi-orthogonal rational functions ⋮ An extension of the associated rational functions on the unit circle ⋮ Rational interpolation. I: Least square convergence ⋮ The existence and construction of rational Gauss-type quadrature rules ⋮ Rational interpolation. II: Quadrature and convergence ⋮ Orthogonal rational functions with complex poles: The Favard theorem ⋮ Computing rational Gauss-Chebyshev quadrature formulas with complex poles: The algorithm

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