Impossibility of fast stable approximation of analytic functions from equispaced samples

Rodrigo Platte, Lloyd N. Trefethen, Arno B J Kuijlaars

Research output: Contribution to journalArticlepeer-review

74 Scopus citations

Abstract

It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions. To avoid instability, one must settle for root-exponential convergence. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992.

Original languageEnglish (US)
Pages (from-to)308-318
Number of pages11
JournalSIAM Review
Volume53
Issue number2
DOIs
StatePublished - 2011

Keywords

  • Gibbs phenomenon
  • Interpolation
  • Lanczos iteration
  • Radial basis functions
  • Runge phenomenon

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics

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