A united approach to accelerating trigonometric expansions

Baszenski, Günter; Delvos, Franz-Jürgen; Tasche, Manfred

doi:10.1016/0898-1221(95)00084-4

Cited by 26 publications

(10 citation statements)

References 6 publications

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“…KE-method and other approaches to the acceleration of convergence of Fourier series have been developed in different directions by many researchers (see [3][4][5], [7][8][9][10][11][12][13][14][15][16][17][18] and their links). In particular, an algorithm is given in [9] possessing a superconvergency (faster than any power-law convergence ) for infinitely smooth functions.…”

Section: 2mentioning

confidence: 99%

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

Nersessian

2022

Armen.J.Math.

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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.

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Section: 2mentioning

confidence: 99%

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

Nersessian

2022

Armen.J.Math.

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“…Lanczos and Krylov [6,31,32] independently observed in the mid-twentieth century that the Fourier coefficients of such ''piecewise analytic" functions have a ''Fourier coefficient asymptotic expansion" (FACE) [34,35,13] in inverse powers of n. a n $ 1 …”

Section: The Basic Ideamentioning

confidence: 99%

Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of

Boyd

2009

Journal of Computational Physics

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“…(8) to converge uniformly and polynomially over the interval, including the end points. As a matter of fact, the polynomial subtraction techniques have been employed by mathematicians as a means to accelerate the convergence of the Fourier series expansion for an explicitly defined function [26][27][28].…”

Section: An Approximate Solution Based On the Rayleigh-ritz Proceduresmentioning

confidence: 99%