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.
Contents
User Guide
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
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.
What Do You Use for Basis Functions and Approximation?
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.
Get
the MATLAB code
Published with MATLAB® 7.9
I work in optics, so I use Zernike polynomials all the time. Also, I have used Pade functions a few times.
Background: I try to create optimal drug development strategies at the portfolio level by integrating strategic, statistical, clinical, financial and commercial perspectives in a single dynamic framework. Part of the problem is shifting of projected revenue and cost curves in time which are often provided as per-year values.
Answer to Loren’s question: I use splines for shifting (take annual data, create curve, shift curve respecting patent expiry brick wall, and recalc annual sales or costs). I have no idea what wawelets or Cheb functions are.
Thanks, Loren, for you posts which I always read w pleasure.
Claus
Cambridge, MA
Finance, Optimization, Statistics tool packs