Parallel schemes of computation for Bernstein coefficients and their application

Abstract

In the note we have established an approach to the range evaluation of a function over an interval. That problem is related to solving nonlinear system of algebraic equations with use of interval analysis techniques. Ranges of values of the nonlinear functions are approximated by coefficients of Bernstein polynomials. We have derived that coefficients of Bernstein polynomials are effectively calculated in some parallel process. We have used this approach in the algorithm for obtaining all solutions of nonlinear equations. The algorithm is based on box-bisection interval searching. Numerical studies are also reported in order to verify presented algorithm.