| Abstract:The tensor is a generalization of the matrix,being applied in many scientific fields.H-tensors have special structure and properties,which make it to play an indispensable role in tensor analysis and operation.Therefore,the structural properties,judgment criteria,and iterative algorithms of H-tensors have been widely concerned by experts and scholars in recent years.Due to the wide application of even order homogeneous polynomial in medical imaging,stability analysis of nonlinear self-made system,feasibility analysis of multivariate network,etc.,it is more and more important to determine whether an even order homogeneous polynomial is positive.Since the H-tensor is consistent with the tensor,the problem of positive polynomials can be solved based on this.This paper studies the determination of H-tensors on the basis of the matrixtheory study.Firstly,by constructing different diagonal matrix transformation factors and combining with the scaling technique of the inequality,several practical criterions of H-tensors are given.Moreover,numerical examples are presented after each criterion to show the rationality and validity of these criteria.Second,we obtain an iterative algorithm of H-tensor and prove that the algorithm stops in finite steps,which shows the effectiveness of the non-parametric iterative discrimination algorithm of H-tensor.Finally,as an important application of these judgment methods,the positive criterion of real symmetric tensors of even order,namely the positive problems of higher even multidimensional homogeneous polynomials.Some numerical examples are also given after each criterion to illustrate the superiority of the results. |
