Nersessian, Anry (2018) On an Over-Convergence Phenomenon for Fourier series. Basic Approach. Armenian Journal of Mathematics, 10 (9). pp. 1-22. ISSN 1829-1163
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Abstract
This paper is devoted to the acceleration of the convergence of the partial sums of the classical Fourier series for the sufficiently smooth functions. Some universal and adaptive algorithms are constructed and studied. It is shown that the use of a finite number of Fourier coefficients makes it possible exact approximation of a given function from an infinite-dimensional set of quasi-polynomials. In this sense, we call the corresponding essentially nonlinear algorithms as over-convergent. The proposed algorithms are implemented using Wolfram Mathematica system. Numerical results demonstrate their effectiveness.
| Item Type: | Article |
|---|---|
| Subjects: | 42-xx Fourier analysis 65-xx Numerical analysis |
| ID Code: | 832 |
| Deposited By: | Professor Anry Nersesyan |
| Deposited On: | 26 Oct 2018 17:16 |
| Last Modified: | 01 Nov 2018 18:40 |
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