On Clenshaw's method and a generalisation to Faber series

DOI10.1007/BF01400888zbMath0628.34009OpenAlexW2016327917MaRDI QIDQ1093067

S. W. Ellacott, Edward B. Saff

Publication date: 1988

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133249

zbMATH Keywords

Chebyshev polynomialshypergeometric functionBessel functionChebyshev seriesFaber polynomial

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) 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) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Ordinary differential equations in the complex domain (34M99) Software, source code, etc. for problems pertaining to special functions (33-04)

Related Items

Complex polynomial approximation by the Lanczos \(\tau\)-method: Dawson's integral, A note on the tau-method approximations for the Bessel functions \(Y_ 0(z)\) and \(Y_ 1(z)\), The Faber Polynomials for Annular Sectors, Symbolic and numerical computation on Bessel functions of complex argument and large magnitude

Cites Work

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• Polynomial approximations in the complex plane
• The special functions and their approximations. Vol. I, II
• The Polynomial Carathéodory—Fejér Approximation Method for Jordan Regions
• Computation of Faber Series With Application to Numerical Polynomial Approximation in the Complex Plane
• On the Faber Transform and Efficient Numerical Rational Approximation
• The Faber Polynomials for Circular Sectors