FOURTH-ORDER PARTIALLY SYMMETRIC TENSORS: THEORY AND ALGORITHM

摘要

With the coming of the big data era, high-order tensors have received much attention of researches in recent years, and this makes it to be a useful tool in data analysis. As a special kind of structured tensor, the fourth-order partially symmetric tensor receives a special concern due to its wide applications in nonlinear elasticity materials. In this review, we will give a survey on recent advances of fourth-order partially symmetric tensors such as M-eigenvalue inclusion intervals, M-positive definiteness, strong ellipticity condition and algorithms for computing the largest M-eigenvalue. Some potential research directions in the future are also listed in the paper.