Driscoll, Tobin A.; Fornberg, Bengt A Padé-based algorithm for overcoming the Gibbs phenomenon. (English) Zbl 0973.65133 Numer. Algorithms 26, No. 1, 77-92 (2001). The authors modify the standard Fourier-Padé technique to account for the general form of the singularity introduced by a discontinuity. The resulting methods exhibit exponential convergence globally for piecewise analytic functions when the jump location(s) are known. Implementation requires just the solution of a linear system, as in standard Padé approximation. Comparisons with other existing techniques are provided. Reviewer: Karel Najzar (Praha) Cited in 3 ReviewsCited in 42 Documents MSC: 65T40 Numerical methods for trigonometric approximation and interpolation 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series Keywords:Padé approximation; Fourier series; Gibbs phenomenon; comparison of methods; exponential convergence PDFBibTeX XMLCite \textit{T. A. Driscoll} and \textit{B. Fornberg}, Numer. Algorithms 26, No. 1, 77--92 (2001; Zbl 0973.65133) Full Text: DOI