Chebfun and numerical quadrature

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