The chebfun system

Chebfun (www.chebfun.org) is an open-source software system for numerical computing with functions. The mathematical basis of Chebfun is piecewise polynomial interpolation implemented with what we call “Chebyshev technology”. Chebfun has extensive capabilities for dealing with linear and nonlinear differential and integral operators, and it also includes continuous analogues of linear algebra notions like QR and singular value decomposition. The Chebfun2 extension works with functions of two variables defined on a rectangle in the xy-plane.

I was one of the main developers/authors of Chebfun versions 2 and 3.

SIAM News article by Nilima Nigam: "Chebfun: Get Out from Under the Hood, and Into the Fast Car" http://www.siam.org/pdf/news/1934.pdf (2011).

Infinitely Smooth Compactly Supported RBFs

A Matlab file that approximates infinitely smooth compactly supported and positive definite kernels in dimensions 1,2, and 3 is available here: CinfCS.m. Please notice that Chebfun is required to used this code: www.chebfun.org.

Reference: R.B. Platte. $C^\infty$ compactly supported and positive definite radial kernels. SIAM J. Sci. Comput. (to appear). (pdf)

Divergence-free kernels

A collection of codes used to generate the results presented in paper below can be found here. These Matlab files were written by Arthur Mitrano.

Reference: A.A. Mitrano, R.B. Platte. A numerical study of divergence-free kernel approximations. Appl. Numer. Math., 96 (2015) 94–107. (pdf)

Stability of RBF methods for convection problems on the circle and sphere

A collection of MATLAB files to generate the results presented in paper below can be found here: circle_sphere_convection_code.zip.

Reference: J.M. Martel, R.B. Platte. Stability of radial basis function methods for convection problems on the circle and sphere. J. Sci. Comput. (submitted). (pdf)