Determination of optimal parameters for the Chebyshev-Gegenbauer reconstruction method

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

We propose a, new strategy for choosing the optimal parameters for the Gegenbauer reconstruction method based on Chebyshev spectral coefficients under different assumptions on the smoothness of the function f. These parameters are optimal in the sense that the bounds on the truncation and regularization errors were forced to be equal. This strategy is independent on the number of terms N in the Chebyshev expansion of the function f and guarantees exponential convergence as N → ∞ of the Gegenbauer series to f on the intervals of smoothness. The effectiveness of this strategy and exponential convergence are confirmed by numerical examples for functions with varying degrees of smoothness.

Original languageEnglish (US)
Pages (from-to)1187-1198
Number of pages12
JournalSIAM Journal on Scientific Computing
Volume25
Issue number4
DOIs
StatePublished - Dec 1 2003

Keywords

  • Chebyshev expansion
  • Exponential convergence
  • Gegenbauer reconstruction

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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