Accurate polynomial interpolation by using the Bernstein basis

摘要

The problem of polynomial interpolation with the Lagrange-type data when using the Bernstein basis instead of the monomial basis is addressed. The extension to the bivariate case, which leads to the use of a generalized Kronecker product, is also developed. In addition to the matricial description of the solution and the proof of unisolvence, algorithms for the computation of the coefficients of the interpolating polynomial are presented. Numerical experiments illustrating the advantage of computing with Bernstein-Vandermonde matrices instead of with Vandermonde matrices are included.