Chebfun and numerical quadrature

Hale, Nicholas; Trefethen, Lloyd N.

Chebfun and numerical quadrature

Type

Article

Authors

Hale, Nicholas
Trefethen, Lloyd N.

KAUST Grant Number

KUK-C1-013-04

Online Publication Date

2012-07-24

Print Publication Date

2012-09

Date

2012-07-24

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.

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⁾.