Finding all isolated solutions to polynomial systems using HOMPACK
ACM Transactions on Mathematical Software (TOMS)
The cheater's homotopy: an efficient procedure for solving systems of polynomial equations
SIAM Journal on Numerical Analysis
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
The method of resultants for computing real solutions of polynomial systems
SIAM Journal on Numerical Analysis
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
| Hi-index | 7.29 |
We present a new practicable method for approximating all real zeros of polynomial systems using the resultants method. It is based on the theory of multi-resultants. We build a sparse linear system. Then, we solve it by the quasi-minimal residual method. Once our test function changes its sign, we apply the secant method to approximate the root. The unstable calculation of the determinant of the large sparse matrix is replaced by solving a sparse linear system. This technique will be able to take advantage of the sparseness of the resultant matrix. Theoretical and numerical results are presented.