Chebfun 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”. The foundations are described, with Chebfun examples, in the book Approximation Theory and Approximation Practice. 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 x-y plane. To get a sense of the breadth and power of Chebfun, a great place to start is by looking at our Examples.

Chebfun is compatible with MATLAB 7.8 (R2009a) and later.

To install, you can either clone the directory with Git or download a .zip file. Note that a call to clear classes is required if you had a previous version of Chebfun installed.

Download a .zip of Chebfun from

• https://github.com/chebfun/chebfun/archive/master.zip

After unzipping, you will need to add Chebfun to the MATLAB path. You can do this either (a) by typing

addpath(chebfunroot), savepath

where chebfunroot is the path to the unzipped directory, (b) by selecting the chebfun directory with the pathtool command, or (c) though the File > Set Path... dialog from the MATLAB menubar.

To clone the Chebfun repository, first navigate in a terminal to where you want the repository cloned, then type

git clone https://github.com/chebfun/chebfun.git

To use Chebfun in MATLAB, you will need to add the chebfun directory to the MATLAB path as above.

We recommend taking a look at the Chebfun Guide and the Examples collection. The Guide is an in-depth tour of Chebfun's mathematical capabilities. The Examples, which number well over one hundred, illustrate everything from rootfinding to optimization to nonlinear differential equations and vector calculus. Many users use the Examples as templates for their own problems.

To get a taste of what computing with Chebfun is like, type

x = chebfun('x');

and start playing. The variable x is a chebfun and can be manipulated in a way that feels symbolic, although everything Chebfun does is numeric. So try, for instance:

f = sin(12*x).*exp(-x);         % A function on [-1, 1]
g = max(f, 1./(x+2));           % The max of f and 1./(x+2)
plot(g)                         % A function with discontinuous derivative
sum(g)                          % The integral of g
plot(diff(g))                   % The derivative of g
h = g + x - .8;                 % A function with several roots in [-1, 1]
rr = roots(h);                  % Compute the roots of h
plot(h, 'k', rr, h(rr), 'ro')   % Plot h and its roots

See LICENSE.txt for Chebfun's licensing information.