New criteria-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 identifing the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose an iterative scheme for identifying ℋ-tensor and prove that the algorithm can terminate within finite iterative steps. Some numerical examples are provided to illustrate the efficiency and validity of methods.

Keywords

• positive definiteness
• homogeneous multivariate form
• ℋ-tensors
• generalized diagonal dominance
• iterative scheme
• 15a69
• 15a18
• 65f15
• 65h17