Bounds for Absolute Positiveness of Multivariate Polynomials

A multivariate polynomialP(x1, …,xn) with real coefficients is said to beabsolutelypositivefrom a real numberBiff it and all of its non-zero partial derivatives of every order are positive forx1,…,xn B. We call suchBaboundfor the absolute positivenessofP. This paper provides a simple formula for computing such bounds. We also prove that the resulting bounds are guaranteed to be close to the optimal ones.