Bit complexity for multi-homogeneous polynomial system solving Application to polynomial minimization.
Journal of Symbolic Computation(2018)
摘要
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 is finite. The algorithm is probabilistic and a probability analysis is provided.
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关键词
Polynomial system solving,Multi-homogeneous systems,Polynomial optimization
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