On a Convergence of Rational Approximations by the Modified Fourier Basis

  • Tigran Bakaryan Institute of mathematics, of National Academy of Sciences of Armenia Bagramian ave. 24B, 0019 Yerevan, Armenia

Abstract

We continue investigations of the modified-trigonometric-rational approximations that arise while accelerating the convergence of the modified Fourier expansions by means of rational corrections. Previously, we investigated the pointwise convergence of the rational approximations away from the endpoints and the $L_2$-convergence on the entire interval. Here, we study the convergence at the endpoints and derive the exact constants for the main terms of asymptotic errors. We show that the Fourier-Pade approximations are much more accurate in all frameworks than the modified expansions for sufficiently smooth functions. Moreover, we consider a simplified version of the rational approximations and explore the optimal values of parameters that lead to better accuracy in the framework of the $L_2$-error. Numerical experiments perform comparisons of the rational approximations with the modified Fourier expansions.

Published
2017-12-26
How to Cite
Bakaryan, T. (2017). On a Convergence of Rational Approximations by the Modified Fourier Basis. Armenian Journal of Mathematics, 9(2), 68-83. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/166
Section
Articles