Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The basic facts about the Barycentric, -ernstein, -ezier form of a multivariate polynomial are recorded and, in part, proved. These include evaluation de Casteliaus algorithm, differentiation and integration, product, degree raising, change of the underlying simplex, and the behavior on the boundary of the underlying simplex, with application to the construction of smooth pp functions on a given triangulation. Some effort has gone into making the notation fully reflect the symmetries and structure of this form. In particular, the description of this form in terms of difference operators is stressed. Keywords Piecewise polynomials Linear interpolation.
- Numerical Mathematics