An iterative algorithm based on strong H-tensors for identifying positive definiteness of irreducible homogeneous polynomial forms

摘要

Identifying the positive definiteness of an even-degree homogeneous polynomial form arises in various applications, such as evolutionary game dynamics, automatical control, magnetic resonance imaging, and spectral hypergraph theory. However, it is difficult to determine whether a given homogeneous polynomial is positive definite or not because the problem is H-hard. In this paper, an iterative algorithm of identifying the positive definiteness of irreducible homogeneous polynomial forms is proposed by identifying strong H-tensors with weakly irreducibility. The validity of the iterative algorithm is proved theoretically. Experimental results on multilinear systems, high-order Markov chains and symmetric multi-player games are presented to illustrate the applications of the proposed methods. (C) 2019 Elsevier B.V. All rights reserved.