A bound on the minimum of a real positive polynomial over the standard simplex

Details A bound on the minimum of a real positive polynomial over the standard simplex A bound on the minimum of a real positive polynomial over the standard simplex

2009-02-19

arxiv.org/abs/0902.3304v1

Computer Science

Symbolic Computation

Scientific paper

We consider the problem of bounding away from 0 the minimum value m taken by a polynomial P of Z[X_1,...,X_k] over the standard simplex, assuming that m>0. Recent algorithmic developments in real algebraic geometry enable us to obtain a positive lower bound on m in terms of the dimension k, the degree d and the bitsize of the coefficients of P. The bound is explicit, and obtained without any extra assumption on P, in contrast with previous results reported in the literature.

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