New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms

Abstract

Positive definite polynomials are important in the field of optimization. H-tensors play an important role in identifying the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose some new criterion for identifying H-tensor. As applications, we give new conditions for identifying positive definiteness of the even-order homogeneous multivariate form. At last, some numerical examples are provided to illustrate the efficiency and validity of new methods.

Keywords

• homogeneous multivariate form
• positive definiteness
• h-tensors
• irreducible
• non-zero element chain