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A Padé-based algorithm for overcoming the Gibbs phenomenon. (English) Zbl 0973.65133

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.

MSC:

65T40 Numerical methods for trigonometric approximation and interpolation
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
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