TY - JOUR
T1 - Chebfun and numerical quadrature
AU - Hale, Nicholas
AU - Trefethen, Lloyd N.
N1 - 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.
PY - 2012/7/24
Y1 - 2012/7/24
N2 - 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.
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.
UR - http://hdl.handle.net/10754/597764
UR - http://link.springer.com/10.1007/s11425-012-4474-z
UR - http://www.scopus.com/inward/record.url?scp=84865553498&partnerID=8YFLogxK
U2 - 10.1007/s11425-012-4474-z
DO - 10.1007/s11425-012-4474-z
M3 - Article
SN - 1674-7283
VL - 55
SP - 1749
EP - 1760
JO - Science China Mathematics
JF - Science China Mathematics
IS - 9
ER -