An iterative scheme for testing the positive definiteness of multivariate homogeneous forms

摘要

A positive-definite homogeneous multivariate form plays a critical role in the medical imaging and automatic control, and the definiteness of this form can be identified by a special structure tensor. In this paper, we first state the equivalence between the positive-definite multivariate form and the corresponding tensor and account for the links between the positive-definite tensor with a strong H-tensor. Then based on weak reducibility, some criteria were provided to identify strong H-tensors. Furthermore, with these relations, we establish an iterative scheme to identify the positive-definite multivariate homogeneous form and prove it is theoretically valid. Numerical experiments were given to illustrate the practicality of the scheme.