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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.
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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