Multipolynomial resultant algorithms
Journal of Symbolic Computation
Algebraic and numeric techniques in modeling and robotics
Algebraic and numeric techniques in modeling and robotics
Concise parallel Dixon determinant
Computer Aided Geometric Design
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
Ray tracing parametric patches
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Implicit and parametric curves and surfaces for computer aided geometric design
Implicit and parametric curves and surfaces for computer aided geometric design
Corner edge cutting and Dixon A-resultant quotients
Journal of Symbolic Computation
Computing multivariate approximate GCD based on Barnett's theorem
Proceedings of the 2009 conference on Symbolic numeric computation
Kukles revisited: Advances in computing techniques
Computers & Mathematics with Applications
Formal power series and loose entry formulas for the dixon matrix
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
On the mixed cayley-sylvester resultant matrix
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
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Efficient algorithms are derived for computing the entries of theBezout resultant matrix for two univariate polynomials of degree nand for calculating the entries of the Dixon-Cayley resultantmatrix for three bivariate polynomials of bidegree (m, n). Standardmethods based on explicit formulas require O(n3)additions and multiplications to compute all the entries of theBezout resultant matrix. Here we present a new recursive algorithmfor computing these entries that uses only O(n2)additions and multiplications. The improvement is even moredramatic in the bivariate setting. Established techniques based onexplicit formulas require O(m4n4) additionsand multiplications to calculate all the entries of theDixon-Cayley resultant matrix. In contrast, our recursive algorithmfor computing these entries uses only O(m2n3)additions and multiplications. Copyright 2002 Academic Press