On a fast convergence of the rational-trigonometric-polynomial interpolation. (English) Zbl 1268.65019

Poghosyan, Arnak

Adv. Numer. Anal. 2013, Article ID 315748, 13 p. (2013).

Summary: We consider the convergence acceleration of the Krylov-Lanczos interpolation by rational correction functions and investigate the convergence of the resultant parametric rational-trigonometric-polynomial interpolation. Exact constants of asymptotic errors are obtained in the regions away from discontinuities, and fast convergence of the rational-trigonometric-polynomial interpolation compared to the Krylov-Lanczos interpolation is observed. Results of numerical experiments confirm theoretical estimates and show how the parameters of the interpolations can be determined in practice.

MSC:

65D05	Numerical interpolation
41A05	Interpolation in approximation theory
65T40	Numerical methods for trigonometric approximation and interpolation
42A15	Trigonometric interpolation
41A10	Approximation by polynomials

Keywords:

convergence acceleration; Krylov-Lanczos interpolation; rational correction functions; rational-trigonometric-polynomial interpolation; numerical experiments

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