A mapped polynomial method for high-accuracy approximations on arbitrary grids

Ben Adcock, Rodrigo Platte

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

The focus of this paper is the approximation of analytic functions on compact intervals from their pointwise values on arbitrary grids. We introduce a new method for this problem based on mapped polynomial approximation. By careful selection of the mapping parameter, we ensure both high accuracy of the approximation and an asymptotically optimal scaling of the polynomial degree with the grid spacing. As we explain, efficient implementation of this method can be achieved using nonuniform fast Fourier transforms. Numerical results demonstrate the efficiency and accuracy of this approach.

Original languageEnglish (US)
Pages (from-to)2256-2281
Number of pages26
JournalSIAM Journal on Numerical Analysis
Volume54
Issue number4
DOIs
StatePublished - 2016

Keywords

  • Analytic functions
  • Equispaced nodes
  • Runge phenomenon
  • Scattered data
  • Spectral methods

ASJC Scopus subject areas

  • Numerical Analysis

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