Chebfun and numerical quadrature

Nicholas Hale; Lloyd N. Trefethen

doi:10.1007/s11425-012-4474-z

Chebfun and numerical quadrature

Nicholas Hale, Lloyd N. Trefethen

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

25 Scopus citations

Abstract

Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun's fast capabilities for Clenshaw-Curtis and also Gauss-Legendre, -Jacobi, -Hermite, and -Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation. © 2012 Science China Press and Springer-Verlag Berlin Heidelberg.

Original language	English (US)
Pages (from-to)	1749-1760
Number of pages	12
Journal	Science China Mathematics
Volume	55
Issue number	9
DOIs	https://doi.org/10.1007/s11425-012-4474-z
State	Published - Jul 24 2012
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This work was supported by the MathWorks, Inc., King Abdullah University of Science and Technology (KAUST) (Award No. KUK-C1-013-04), and the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC (Grant Agreement No. 291068) 2).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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abstract = "Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun's fast capabilities for Clenshaw-Curtis and also Gauss-Legendre, -Jacobi, -Hermite, and -Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation. {\textcopyright} 2012 Science China Press and Springer-Verlag Berlin Heidelberg.",

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AB - Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun's fast capabilities for Clenshaw-Curtis and also Gauss-Legendre, -Jacobi, -Hermite, and -Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation. © 2012 Science China Press and Springer-Verlag Berlin Heidelberg.

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Chebfun and numerical quadrature

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