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TitleDivision algorithms for Bernstein polynomials
Author(s) Laurent Buse, Ronald N. Goldman
TypeArticle in Journal
AbstractThree division algorithms are presented for univariate Bernstein polynomials: an algorithm for finding the quotient and remainder of two univariate polynomials, an algorithm for calculating the GCD of an arbitrary collection of univariate polynomials, and an algorithm for computing a μ-basis for the syzygy module of an arbitrary collection of univariate polynomials. Division algorithms for multivariate Bernstein polynomials and analogues in the multivariate Bernstein setting of Gröbner bases are also discussed. All these algorithms are based on a simple ring isomorphism that converts each of these problems from the Bernstein basis to an equivalent problem in the monomial basis. This isomorphism allows all the computations to be performed using only the original Bernstein coefficients; no conversion to monomial coefficients is required.
URL http://www.sciencedirect.com/science/article/pii/S0167839607001112
JournalComputer Aided Geometric Design
Pages850 - 865
NoteClassical Techniques for Applied Geometry
Translation No
Refereed No