Piecewise-smooth chebfuns

Ricardo Pachón; Rodrigo B. Platte; Lloyd N. Trefethen

doi:10.1093/imanum/drp008

Piecewise-smooth chebfuns

Ricardo Pachón, Rodrigo B. Platte, Lloyd N. Trefethen

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

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 language	English (US)
Pages (from-to)	898-916
Number of pages	19
Journal	IMA Journal of Numerical Analysis
Volume	30
Issue number	4
DOIs	https://doi.org/10.1093/imanum/drp008
State	Published - Oct 2010
Externally published	Yes

Keywords

Chebyshev series
barycentric interpolation
chebfun system
edge detection

ASJC Scopus subject areas

General Mathematics
Computational Mathematics
Applied Mathematics

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10.1093/imanum/drp008

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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.",

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author = "Ricardo Pach{\'o}n and Platte, {Rodrigo B.} and Trefethen, {Lloyd N.}",

year = "2010",

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AU - Pachón, Ricardo

AU - Platte, Rodrigo B.

AU - Trefethen, Lloyd N.

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AB - 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.

KW - Chebyshev series

KW - barycentric interpolation

KW - chebfun system

KW - edge detection

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Piecewise-smooth chebfuns

Abstract

Keywords

ASJC Scopus subject areas

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