The Projected Newton Iteration Approach for Computing the Nonnegative Z-Eigenpairs of Nonnegative Tensors

Abstract

In this paper, we propose a new projected Newton iteration for computing the nonnegative Z-eigenpairs of nonnegative tensors. We show that the required iteration has a local quadratic convergence. More specially, the formulation aims to solve the tensor equation arising from the multilinear PageRank problem. Numerical experiments are provided to illustrate the effectiveness and superiority of the proposed approach.