Coefficient-parameter polynomial continuation
Applied Mathematics and Computation
Finding all isolated solutions to polynomial systems using HOMPACK
ACM Transactions on Mathematical Software (TOMS)
The membership problem for unmixed polynomial ideals is solvable in single exponential time
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
A new start system for solving deficient polynomial systems using continuation
Applied Mathematics and Computation
Finding all isolated zeros of polynomial systems in Cn via stable mixed volumes
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Minimizing multi-homogeneous Bézout numbers by a local search method
Mathematics of Computation
Some Effectivity Problems in Polynomial Ideal Theory
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
| Hi-index | 7.29 |
Precondition plays a critical role in the numerical methods for large and sparse linear systems. It is also true for nonlinear algebraic systems. In this paper incomplete Grobner basis (IGB) is proposed as a preconditioner of homotopy methods for polynomial systems of equations, which transforms a deficient system into a system with the same finite solutions, but smaller degree. The reduced system can thus be solved faster. Numerical results show the efficiency of the preconditioner.