Reduction of the Gibbs phenomenon for smooth functions with jumps by the ε-algorithm

[摘要] Recently, Brezinski has proposed to use Wynn's epsilon-algorithm in order to reduce the Gibbs phenomenon for partial Fourier sums of smooth functions with jumps, by displaying very convincing numerical experiments. In the present paper we derive analytic estimates for the error corresponding to a particular class of hypergeometric functions, and obtain the rate of column convergence for such functions, possibly perturbed by another sufficiently differentiable function. We also analyze the connection to Pade-Fourier and Pade-Chebyshev approximants, including those recently studied by Kaber and Maday. (C) 2007 Elsevier B.V. All tights reserved.

[发布日期] 2008-10-01

[效力级别]  Proceedings Paper

[关键词] Fourier series;Gibbs phenomenon;convergence acceleration;epsilon-algorithm;Pade-Fourier approximants;Pade-Chebyshev approximants