On a convergence of the Fourier-Pade approximation


  • Arnak Poghosyan Institute of Mathematics, National Academy of Sciences of Armenia Bagramian ave. 24b, 0019 Yerevan, Armenia


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.




How to Cite

Poghosyan, A. (2013). On a convergence of the Fourier-Pade approximation. Armenian Journal of Mathematics, 4(2), 49-79. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/85