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    Chebfun and numerical quadrature

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    Type
    Article
    Authors
    Hale, Nicholas
    Trefethen, Lloyd N.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2012-07-24
    Online Publication Date
    2012-07-24
    Print Publication Date
    2012-09
    Permanent link to this record
    http://hdl.handle.net/10754/597764
    
    Metadata
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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. © 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.
    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>.
    Publisher
    Springer Nature
    Journal
    Science China Mathematics
    DOI
    10.1007/s11425-012-4474-z
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11425-012-4474-z
    Scopus Count
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