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

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader


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

Repository Staff Only: item control page