Structured matrix methods for CAGD: An application to computing the resultant of polynomials in the Bernstein basis

We devise a fast fraction-free algorithm for the computation of the triangular factorization of Bernstein-Bezoutian matrices with entries over an integral domain. Our approach uses the Bareiss fraction-free variant of Gaussian elimination, suitably modified to take into account the structural properties of Bernstein-Bezoutian matrices. The algorithm can be used to solve problems in algebraic geometry that arise in computer aided geometric design and computer graphics. In particular, an example of the application of this algorithm to the numerical computation of the intersection points of two planar rational Bezier curves is presented. Copyright (c) 2005 John Wiley & Sons, Ltd.