Handle URI:
http://hdl.handle.net/10754/597764
Title:
Chebfun and numerical quadrature
Authors:
Hale, Nicholas; Trefethen, Lloyd N.
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.
Citation:
Hale N, Trefethen LN (2012) Chebfun and numerical quadrature. Sci China Math 55: 1749–1760. Available: http://dx.doi.org/10.1007/s11425-012-4474-z.
Publisher:
Springer Nature
Journal:
Science China Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
24-Jul-2012
DOI:
10.1007/s11425-012-4474-z
Type:
Article
ISSN:
1674-7283; 1869-1862
Sponsors:
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) <SUP>2)</SUP>.
Appears in Collections:
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Full metadata record

DC FieldValue Language
dc.contributor.authorHale, Nicholasen
dc.contributor.authorTrefethen, Lloyd N.en
dc.date.accessioned2016-02-25T12:56:18Zen
dc.date.available2016-02-25T12:56:18Zen
dc.date.issued2012-07-24en
dc.identifier.citationHale N, Trefethen LN (2012) Chebfun and numerical quadrature. Sci China Math 55: 1749–1760. Available: http://dx.doi.org/10.1007/s11425-012-4474-z.en
dc.identifier.issn1674-7283en
dc.identifier.issn1869-1862en
dc.identifier.doi10.1007/s11425-012-4474-zen
dc.identifier.urihttp://hdl.handle.net/10754/597764en
dc.description.abstractChebfun 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.en
dc.description.sponsorshipThis 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) <SUP>2)</SUP>.en
dc.publisherSpringer Natureen
dc.subjectbarycentric interpolation formulaen
dc.subjectChebfunen
dc.subjectClenshaw-Curtis quadratureen
dc.subjectfractional calculusen
dc.subjectGauss quadratureen
dc.subjectRiemann-Liouville integralen
dc.titleChebfun and numerical quadratureen
dc.typeArticleen
dc.identifier.journalScience China Mathematicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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