ABSTRACT 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… Click to show full abstract
ABSTRACT 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.
               
Click one of the above tabs to view related content.