On an Over-Convergence Phenomenon for Fourier series. Basic Approach

Author(s)

On an Over-Convergence Phenomenon for Fourier series. Basic Approach Anry Nersessian

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.

DOI: 10.52737/18291163-2018.10.9-1-22 Armenian Journal of Mathematics, 10(9) 1-22

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Keywords

Fourier series, biorthogonalization, acceleration of convergence, spectral methods, adaptive algorithms, over-convergence, detection of periodicities

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