Chebyshev expansion on intervals with branch points with application to the root of Kepler's equation: A Chebyshev-Hermite-Padé method

DOI10.1016/j.cam.2008.02.007zbMath1152.65024OpenAlexW1991650118MaRDI QIDQ2378246

John P. Boyd

Publication date: 7 January 2009

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.2008.02.007

zbMATH Keywords

Kepler equationChebyshevHermite-Padé approximant

Mathematics Subject Classification ID

Algorithms for approximation of functions (65D15)

Related Items

Upper bounds for the moduli of zeros of Hermite-Padé approximations for a set of exponential functions, Asymptotics of diagonal Hermite-Padé polynomials for the collection of exponential functions, Numerical analytic continuation, New series for the cosine lemniscate function and the polynomialization of the lemniscate integral, Padé approximants of special functions, Super-Gaussian BSS using fast-ICA with Chebyshev-Padé approximant, The asymptotic form of the Hermite-Padé approximations for a system of Mittag-Leffler functions

Uses Software

• VECTOR_PADE

Cites Work

• Rootfinding for a transcendental equation without a first guess: polynomialization of Kepler's equation through Chebyshev polynomial expansion of the sine
• The convergence of Newton-Raphson iteration with Kepler's equation
• Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation
• Shafer (Hermite-Padé) approximants for functions with exponentially small imaginary part with application to equatorial waves with critical latitude.
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• A Chebyshev polynomial interval-searching method (``Lanczos economization) for solving a nonlinear equation with application to the nonlinear eigenvalue problem
• Computing real roots of a polynomial in Chebyshev series form through subdivision
• The special functions and their approximations. Vol. I, II
• Algorithm 766: experiments with a weakly stable algorithm for computing Padé-Hermite and simultaneous Padé approximants
• Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: Application to anharmonic oscillators
• Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding
• Numerical Polynomial Algebra
• Roots of Polynomials Expressed in Terms of Orthogonal Polynomials
• On Quadratic Approximation
• Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions
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