Piecewise-smooth chebfuns

Piecewise-smooth chebfuns

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 automa...

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Veröffentlicht in:IMA journal of numerical analysis 2010-10, Vol.30 (4), p.898-916
Hauptverfasser: Pachón, Ricardo, Platte, Rodrigo B., Trefethen, Lloyd N.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Approximations and expansions
barycentric interpolation
chebfun system
Chebyshev series
Edge detection
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematics
Matlab
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Object oriented
Object-oriented programming
Real functions
Sciences and techniques of general use
Subdivisions
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Beschreibung
Zusammenfassung: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].
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/drp008