On a convergence of the Fourier-Pade interpolation
We investigate convergence of the rational-trigonometric-polynomial interpolation that performs convergence acceleration of the classical trigonometric interpolation by sequential application of polynomial and rational correction functions. Unknown parameters of the rational corrections are determined along the ideas of the Fourier-Pade approximations. The resultant interpolation we call as Fourier-Pade interpolation and investigate its convergence in the regions away from singularities. Comparison with other rational-trigonometric-polynomial interpolations outlines the convergence properties of the Fourier-Pade interpolation.
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