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

  • Anry Nersessian Institute of Mathematics, National Academy of Science of RA
Keywords: Fourier series, biorthogonalization, acceleration of convergence, spectral methods, adaptive algorithms, over-convergence, detection of periodicities

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.

Published
2018-10-26
How to Cite
Nersessian, A. (2018). On an Over-Convergence Phenomenon for Fourier series. Basic Approach. Armenian Journal of Mathematics, 10(9), 0-21. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/213