Piecewise-smooth chebfuns

Ricardo Pachón, Rodrigo Platte, Lloyd N. Trefethen

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

Algorithms are described that make it possible to manipulate piecewise-smooth functions on real intervals numerically with close to machine precision. Break points are introduced in some such calculations at points determined by numerical root finding and in others by recursive subdivision or automatic edge detection. Functions are represented on each smooth subinterval by Chebyshev series or interpolants. The algorithms are implemented in object-oriented Matlab in an extension of the chebfun system, which was previously limited to smooth functions on [- 1, 1]. 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Original languageEnglish (US)
Pages (from-to)898-916
Number of pages19
JournalIMA Journal of Numerical Analysis
Volume30
Issue number4
DOIs
StatePublished - Oct 2010
Externally publishedYes

Fingerprint

Piecewise Smooth Functions
Chebyshev Series
Root-finding
Edge Detection
Interpolants
Subdivision
Smooth function
Object-oriented
MATLAB
Edge detection
Interval

Keywords

  • barycentric interpolation
  • chebfun system
  • Chebyshev series
  • edge detection

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Piecewise-smooth chebfuns. / Pachón, Ricardo; Platte, Rodrigo; Trefethen, Lloyd N.

In: IMA Journal of Numerical Analysis, Vol. 30, No. 4, 10.2010, p. 898-916.

Research output: Contribution to journalArticle

Pachón, Ricardo ; Platte, Rodrigo ; Trefethen, Lloyd N. / Piecewise-smooth chebfuns. In: IMA Journal of Numerical Analysis. 2010 ; Vol. 30, No. 4. pp. 898-916.
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