Completeness of the WDS method in Checking Positivity of Integral Forms

Abstract

Examples show that integral forms can be efficiently proved positive semidefinite by the WDS method, but it was unknown that how many steps of substitutions are needed, or furthermore, which integral forms is this method applicable for. In this paper, we give upper bounds of step numbers of WDS required in proving that an integral form is positive definite, positive semidefinite, or not positive semidefinite, thus deducing that the WDS method is complete.

9 pages

References in corpus (2)

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

Cited by in corpus (2)

• A Complete Method for Checking Hurwitz Stability of a Polytope of Matrices
• Stability Analysis of Linear Uncertain Systems via Checking Positivity of Forms on Simplices