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Optimal rational approximations by the modified Fourier basis. (English) Zbl 1470.41029

Summary: We consider convergence acceleration of the modified Fourier expansions by rational trigonometric corrections which lead to modified-trigonometric-rational approximations. The rational corrections contain some unknown parameters and determination of their optimal values for improved pointwise convergence is the main goal of this paper. The goal was accomplished by deriving the exact constants of the asymptotic errors of the approximations with further elimination of the corresponding main terms by appropriate selection of those parameters. Numerical experiments outline the convergence improvement of the optimal rational approximations compared to the expansions by the modified Fourier basis.

MSC:

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
42A10 Trigonometric approximation
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