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IMA Journal of Numerical Analysis Advance Access published online on July 28, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drp008
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Piecewise-smooth chebfuns

Ricardo Pachón{dagger}, Rodrigo B. Platte{ddagger} and Lloyd N. Trefethen§

Oxford Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK

{dagger} Email: ricp{at}comlab.ox.ac.uk

{ddagger} Email: rodp{at}comlab.ox.ac.uk

§ Corresponding author. Email: lnt{at}comlab.ox.ac.uk

Received on 12 September 2008. Revised on 2 February 2009.


  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].

Key Words: edge detection; chebfun system; Chebyshev series; barycentric interpolation


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