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Oxford University
Mathematical Institute

About Chebfun

What is Chebfun?

Chebfun is a collection of algorithms, and a software system in object-oriented MATLAB, which extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. It also implements continuous analogues of linear algebra notions like the QR decomposition and the SVD, and solves ordinary differential equations. The mathematical basis of the system combines tools of Chebyshev expansions, fast Fourier transform, barycentric interpolation, recursive zerofinding, and automatic differentiation.

Chebfun history

The beginnings

Chebfun began in Oxford's Numerical Analysis Group, part of the Oxford University Mathematical Institute. It started during 2002-2005 as a DPhil research investigation by Zachary Battles, a Rhodes Scholar from the USA, under the supervision of Nick Trefethen. (The idea of overloading Matlab's vectors to functions was first put in writing in an email from Trefethen to Battles of 8 December 2001.) This led to Version 1 of Chebfun, for smooth functions on the interval [-1,1], described in the 2004 SIAM J. Sci. Comp. paper by Battles and Trefethen and in Battles' 2006 thesis.

Zachary Battles

Version 2

The second phase of the project begin in the autumn of 2006 with the beginning of research funding from the UK Engineering and Physical Sciences Research Council (EPSRC). First to join the team was DPhil student Ricardo Pachón, from Colombia, who extended Chebfun to piecewise continuous functions and arbitrary intervals. Automatic subdivision and edge detection were added by Pachón and further developed in collaboration with Rodrigo Platte, from Brazil, a post-doc who arrived in October 2007. Then beginning January 2008, linear operators and solution of differential equations were added to Chebfun, together with integral operators, eigenvalue problems, and exponentials of operators. This was the work of Toby Driscoll, of the University of Delaware, who has led the differential equations side of Chebfun since then. A key collaborator at the beginning of this work was Folkmar Bornemann of the Technical University of Munich. All these developments came together with the release of Chebfun Version 2 in June 2008.

Version 2 Team

Version 3

After the release of Version 2, the project continued to grow. We now had a logo, a version control system, an expanding test suite, a web site, eight chapters of a users guide, half a dozen publications, and quite a few users. Pachón added best approximation by the Remez algorithm and explorations of the complex plane via rational interpolants. Platte introduced mappings that make it possible to treat infinite intervals. Nick Hale joined the Chebfun core team, first as a DPhil student of Trefethen's and then as a postdoc at the Oxford Center for Collaborative Applied Mathematics. Hale added Gauss and other quadrature formulas, even for millions of points, and developed PDE15S for solving nonlinear PDEs (with 1 space and 1 time dimension) within the Chebfun framework. A capability of handling functions that diverge to infinity or have other singularities was added by Oxford DPhil student Mark Richardson, and automatic differentiation and related methods for solving nonlinear boundary-value problems by DPhil student Ásgeir Birkisson in collaboration with Driscoll. Pedro Gonnet, Sheehan Olver, Joris Van Deun and Alex Townsend also became involved. Version 3, a major enhancement of Version 2 incorporating these and other extensions, was coordinated by Rodrigo Platte and Nick Hale and released in December 2009.

Rodrigo Platte & Nick Hale

Version 4

It was now apparent that Chebfun was more than a software package: it was an ongoing and growing software project with half a dozen developers, hundreds of programs, and tens of thousands of lines of code. How could we ensure that it would continue to grow and remain available and up-to-date for a long time to help people solve problems? We were committed to the vision of numerical computing with functions and determined to give that vision as secure as future as possible.

Accordingly, in 2010, we decided that Chebfun should become an open-source project. The software had always been freely available, but we decided to go further and make our operations fully accessible to outsiders, including our Trac bug tracking system, our svn software repository, and discussion groups for communication among interested parties. In particular we would open the door to developers outside Oxford (in addition to Toby Driscoll, who had long been a key player based at the University of Delaware). The open-source Chebfun project would be launched with the release of Chebfun Version 4. Scientifically, the big new features in Version 4 were related to differential equations (led by Driscoll and Hale), the graphical user interface called CHEBGUI (led by Birkisson and Hale), and a new collection of Examples to serve as templates for all kinds of problems (led by Trefethen). Details can be found here.

(Most of the) V4.0 Team

Version 4 was released on 28 February 2011 under a New BSD license. Chebfun is now a fully-fledged open-source project, and outsiders who wish to get involved are encouraged to do so. The Chebfun team is currently led by Nick Hale (Director), Nick Trefethen, and Toby Driscoll.

In September 2012 the Chebfun Team organised a three day workshop in St Anthony's College Oxford entitled Chebfun And Beyond. The theme was building on the success of Chebfun and reaching towards computing with functions in higher dimensions. Below is a picture of (most of) the team present at the workshop.

(Most of the) And Beyond Team

For licensing and copyright purposes, a complete list of the Chebfun contributors is maintained here.

Please contact us with any questions and comments.
Copyright © 2013, The University of Oxford & The Chebfun Team.