The method of resultants for computing real solutions of polynomial systems
SIAM Journal on Numerical Analysis
Sparse elimination and applications in kinematics
Sparse elimination and applications in kinematics
Solving algebraic systems using matrix computations
ACM SIGSAM Bulletin
Matrix computations (3rd ed.)
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
MR: Macaulay Resultant package for Maple
ACM SIGSAM Bulletin
The approximate GCD of inexact polynomials
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
A Rank-Revealing Method with Updating, Downdating, and Applications
SIAM Journal on Matrix Analysis and Applications
Computing the multiplicity structure in solving polynomial systems
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Newton's method with deflation for isolated singularities of polynomial systems
Theoretical Computer Science
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Resultant-based methods for plane curves intersection problems
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
NAClab: a Matlab toolbox for numerical algebraic computation
ACM Communications in Computer Algebra
| Hi-index | 5.23 |
A numerical elimination method is presented in this paper for floating-point computation in polynomial algebra. The method is designed to calculate one or more polynomials in an elimination ideal by a sequence of matrix rank/kernel computation. The method is reliable in numerical computation with verifiable stability and a sensitivity measurement. Computational experiment shows that the method possesses significant advantages over classical resultant computation in numerical stability and in producing eliminant polynomials with lower degrees and fewer extraneous factors. The elimination algorithm combined with an approximate GCD finder appears to be effective in solving polynomial systems for positive dimensional solutions.