Nick Trefethen and a team of colleagues have created a MATLAB software package called chebfun. Version 2 is now available on the File Exchange. Version 3 is available on their site. The package is designed to have syntax very much like regular vector notation in MATLAB, though the entities represent functions.
They accomplished this using some of the newer features of the MATLAB object system. Basically the project extends familiar notions for numbers to the realm of continuous and piecewise continuous functions.
The user guide, on-line, comprises published MATLAB code, and the source is available as well. Chapters include examples
and a set of references for the benefit of those who wish to dive more deeply into the subject matter.
Recent additions include chapters on how to work with infinities (intervals and values) and singularities and nonlinear ODEs.
Examples on this page include how, in version 3, to work with unbounded functions and intervals.
Many people use splines as basis functions for approximations, solving differential equations, and so on. Some people use
wavelets for similar purposes. The package discussed here relies on Chebyshev functions. What do you use? Let me know here.
Published with MATLAB® 7.9