On the minimum of a positive polynomial over the standard simplex

TL;DR

This paper introduces a new lower bound for positive polynomials over the standard simplex, depending on variables, degree, and coefficient bitsize, improving previous bounds for such polynomials.

Contribution

It provides a novel, tighter lower bound for positive polynomials on the simplex based on explicit parameters, surpassing prior bounds.

Findings

New lower bound depends only on variables, degree, and bitsize

Bound improves all previous bounds for positive polynomials on the simplex

Applicable to polynomials with integer coefficients, positive over the simplex

Abstract

We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of R^k, assuming that P is positive on the simplex. This bound depends only on the number of variables, the degree and the bitsize of the coefficients of P and improves all previous bounds for arbitrary polynomials which are positive over the simplex.