An ℋ-tensor-based criteria for testing the positive definiteness of multivariate homogeneous forms

Abstract

A positive definite homogeneous multivariate form plays an important role in the field of optimization, and positive definiteness of the form can be identified by a special structured tensor. In this paper, based on the equivalence between the form and the corresponding tensor, and the links of the positive definiteness of a tensor with ℋ-tensor, we propose an ℋ-tensor-based criterion for identifying the positive definiteness of multivariate homogeneous forms. Some numerical examples are provided to illustrate the efficiency and validity of our results.

Keywords

• homogeneous multivariate form
• positive definiteness
• ℋ-tensors
• diagonally dominant tensors
• irreducible
• non-zero element chain
• 15a69
• 15a18
• 65f15
• 65h17