THE INVERSE EIGENVALUE PROBLEMS OF TENSORS WITH AN APPLICATION IN TENSOR NEARNESS PROBLEMS

摘要

In this paper, we are concerned with the solution of the inverse eigenvalue problem of tensors. The problem under consideration can be regarded as an extension of the matrix case. Explicitly, for several given eigenpairs of a tensor, it is shown that this problem can be converted into solving the system of tensor equations with Einstein product. Using the Moore-Penrose inverses of tensors, we obtain the sufficient and necessary conditions for the solvability of the tensor inverse eigenvalue problem as well as the general solution. As an application of the obtained results, we address the tensor nearness problem corresponding to the tensor inverse eigenvalue problem, and derived its unique solution under some conditions. In order to solve those problems more easily, we also develop the associated iterative approaches originating from the classical conjugate gradient method. The performed numerical results illustrate the feasibility and effectiveness of the proposed methods.