Chebfun and numerical quadrature

Nicholas Hale, Lloyd N. Trefethen

Research output: Contribution to journalArticlepeer-review

16 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 languageEnglish (US)
Pages (from-to)1749-1760
Number of pages12
JournalScience China Mathematics
Volume55
Issue number9
DOIs
StatePublished - Jul 24 2012
Externally publishedYes

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