Details:
Title | Fast Computation of the Bezout and Dixon Resultant Matrices | Author(s) | Eng-Wee Chionh, Ronald N. Goldman, Ming Zhang | Type | Article in Journal | Abstract | Efficient algorithms are derived for computing the entries of the
Bezout resultant matrix for two univariate polynomials of degree n and for calculating the entries of the Dixon-Cayley resultant matrix for three bivariate polynomials of bidegree (m, n). Standard methods based on explicit formulas require O(n^3) additions and multiplications to compute all the entries of the Bezout resultant
matrix. Here we present a new recursive algorithm for computing these entries that uses only O(n^2) additions and multiplications. The improvement is even more dramatic in the bivariate setting. Established techniques based on explicit formulas require
O(m^4 n^4) additions and multiplications to calculate all the entries of the Dixon-Cayley resultant matrix. In contrast, our recursive algorithm for computing these entries uses only
O(m^2 n^3) additions and multiplications. | Keywords | Algebraic Geometry, Computer Graphics, Geometric Modeling, Robotiscs, Elimination Theory, Resultant | Length | 17 | Copyright | Elsevier Science Ltd. |
File |
| URL |
dx.doi.org/10.1006/jsco.2001.0462 |
Language | English | Journal | Journal of Symbolic Computation | Volume | 33 | Number | 1 | Pages | 13-29 | Year | 2002 | Month | January | Edition | 0 | Translation |
No | Refereed |
No |
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