Armenian Journal of Mathematics

On a Convergence of Rational Approximations by the Modified Fourier Basis

Bakaryan, Tigran (2017) On a Convergence of Rational Approximations by the Modified Fourier Basis. Armenian Journal of Mathematics, 9 (2). pp. 68-83. ISSN 1829-1163

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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.

Item Type:Article
Subjects:41-xx Approximations and expansions
65-xx Numerical analysis
ID Code:797
Deposited By:Professor Anry Nersesyan
Deposited On:22 Dec 2017 12:14
Last Modified:22 Dec 2017 12:14

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