A fast and accurate algorithm for solving a Bernstein-Vandermonde linear system is presented. The algorithm is derived by using results related to the bidiagonal decomposition of the inverse of a totally positive matrix by means of Neville elimination. The use of explicit expressions for the determinants involved in the process serves to make the algorithm both fast and accurate.

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When using bivariate polynomial interpolation for computing the implicit equation of a rational plane algebraic curve given by its parametric equations, the generation of the interpolation data is the most costly of the two stages of the process. In this work a new way of generating those interpolation data with less computational cost is presented. The method is based on an efficient computation of the determinants of certain constant Bézout matrices.