Introduction:

Univariate Chebyshev polynomials are omnipresent in approximation theory and computational mathematics. Much less known are their multivariate cousins, which enjoy most of the beautiful properties of univariate Chebyshev. The multivariate polynomials are defined on domains that are related to triangles (2D) and simplexes (higher dimensions), and are therefore interesting building blocks for multidimensional domain sub-division algorithms.

In these pages we will present literature and software to promote the use of multivariate Chebyshev polynomials in applications.

Software:

Software from the paper “On Multivariate Chebyshev Polynomials and Spectral Approximations on Triangles": ChebyshevA2.tar.bz2