Numerical Algorithms

, Volume 26, Issue 1, pp 77–92 | Cite as

A Padé-based algorithm for overcoming the Gibbs phenomenon

  • Tobin A. Driscoll
  • Bengt Fornberg


Truncated Fourier series and trigonometric interpolants converge slowly for functions with jumps in value or derivatives. The standard Fourier–Padé approximation, which is known to improve on the convergence of partial summation in the case of periodic, globally analytic functions, is here extended to functions with jumps. The resulting methods (given either expansion coefficients or function values) 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. The new methods compare favorably in experiments with existing techniques.

Fourier series Padé approximation interpolation Gibbs phenomenon 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Tobin A. Driscoll
    • 1
  • Bengt Fornberg
    • 2
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Department of Applied MathematicsUniversity of ColoradoBoulderUSA

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