Abstract
An interesting combinatorial (enumeration) problem arises in the initial phase of the polyhedral homotopy continuation method for computing all solutions of a polynomial equation system in complex variables. It is formulated as a problem of finding all solutions of a specially structured system of linear inequalities with a certain additional combinatorial condition. This paper presents a computational method for the problem fully utilizing the duality theory and the simplex method for linear programs, and report numerical results on a single cpu implementation and a parallel cpu implementation of the method.
| Original language | English |
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| Pages (from-to) | 64-82 |
| Number of pages | 19 |
| Journal | Journal of the Operations Research Society of Japan |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2002 |