Name
Abstract | ||
|---|---|---|
Three 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 @m-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 Grobner 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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.cagd.2007.10.003 | Computer Aided Geometric Design |
Keywords | Field | DocType |
division algorithm,univariate polynomial,simple ring isomorphism,original bernstein coefficient,multivariate bernstein setting,bernstein basis,univariate bernstein polynomial,multivariate bernstein polynomial,monomial basis,arbitrary collection,bernstein polynomial | Wilson polynomials,Discrete mathematics,Polynomial arithmetic,Classical orthogonal polynomials,Orthogonal polynomials,Algebra,Discrete orthogonal polynomials,Algorithm,Bernstein polynomial,Hahn polynomials,Difference polynomials,Mathematics | Journal |
Volume | Issue | ISSN |
25 | 9 | Computer Aided Geometric Design |
Citations | PageRank | References |
5 | 0.82 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Busé | 1 | 131 | 14.74 |
| Ron Goldman | 2 | 53 | 7.48 |