Bit complexity for multi-homogeneous polynomial system solving Application to polynomial minimization

Mohab Safey El Din 1 Éric Schost 2
1 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria de Paris
Abstract : Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input system under some genericity assumptions. The assumptions essentially imply that the Jacobian matrix of the system under study has maximal rank at the solution set and that this solution set if finite. The algorithm is probabilistic and a probability analysis is provided. Next, we apply these results to the problem of optimizing a linear map on the real trace of an algebraic set. Under some genericity assumptions, we provide bit complexity estimates for solving this polynomial minimization problem.
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Journal of Symbolic Computation, Elsevier, A Paraître, pp.1-32. 〈10.1016/j.jsc.2017.08.001〉
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Soumis le : samedi 9 décembre 2017 - 12:57:41
Dernière modification le : jeudi 11 janvier 2018 - 06:28:03

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Mohab Safey El Din, Éric Schost. Bit complexity for multi-homogeneous polynomial system solving Application to polynomial minimization. Journal of Symbolic Computation, Elsevier, A Paraître, pp.1-32. 〈10.1016/j.jsc.2017.08.001〉. 〈hal-01319729v2〉

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