Polynomial approximations in the complex plane

DOI10.1016/0377-0427(87)90016-1zbMath0633.65021OpenAlexW2064688147MaRDI QIDQ1096326

John P. Coleman

Publication date: 1987

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(87)90016-1

zbMATH Keywords

Chebyshev polynomialsBessel functionstruncated Chebyshev seriesLanczos tau-methodapproximations for the exponentialpolynomial approximations for analytic functions

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) Algorithms for approximation of functions (65D15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (8)

On Clenshaw's method and a generalisation to Faber series ⋮ Complex polynomial approximation by the Lanczos \(\tau\)-method: Dawson's integral ⋮ Tau-method approximations for the Bessel function \(Y_ 0 (z)\) ⋮ Tau-method approximations for the Bessel function \(Y_ 1 (z)\) ⋮ 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 ⋮ Proxy-GMRES: Preconditioning via GMRES in Polynomial Space

Cites Work

• Near-circularity of the error curve in complex Chebyshev approximation
• Some remarks on uniform asymptotic expansions for Bessel functions
• Near-Minimax Polynomial Approximation in an Elliptical Region
• Chebyshev Methods for Ordinary Differential Equations
• Computation of Faber Series With Application to Numerical Polynomial Approximation in the Complex Plane
• The Faber Polynomials for Circular Sectors
• Complex Chebyshev Polynomials on Circular Sectors with Degree Six or Less
• The Lanczos Tau-method
• Chebyshev Expansions for the Bessel Function J n (z) in the Complex Plane
• Approximations for the Bessel and Struve Functions
• Faber Polynomials and the Faber Series
• Trigonometric Interpolation of Empirical and Analytical Functions
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