Armenian Journal of Mathematics

On a convergence of the Fourier-Pade approximation

Poghosyan, Arnak (2013) On a convergence of the Fourier-Pade approximation. Armenian Journal of Mathematics, 4 (2). pp. 49-79. ISSN 1829-1163

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Abstract

We consider convergence acceleration of the truncated Fourier series by sequential application of polynomial and rational corrections. Polynomial corrections are performed along the ideas of the Krylov-Lanczos approximation. Rational corrections contain unknown parameters which determination is a crucial problem for realization of the rational approximations. We consider approach connected with the Fourier-Pade approximations. This rational-trigonometric-polynomial approximation we continue calling the Fourier-Pade approximation. We investigate its convergence for smooth functions in different frameworks and derive the exact constants of asymptotic errors. Detailed analysis and comparisons of different rational-trigonometric-polynomial approximations are performed and the convergence properties of the Fourier-Pade approximation are outlined. In particular, fast convergence of the Fourier-Pade approximation is observed in the regions away from the endpoints.

Item Type:Article
Subjects:41-xx Approximations and expansions
65-xx Numerical analysis
ID Code:536
Deposited By:Professor Anry Nersesyan
Deposited On:07 Mar 2013 11:48
Last Modified:14 Mar 2013 11:17

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