2018/11/28 by Donghui Li, Dong-Hui Li, Hong-Bo Guan +5
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Tensor decomposition and applications #math.OC
paper · pdf · doi:10.48550/arxiv.1811.11343
openalex publication_date 2018/11/28 · arxiv created 2018/12/25 · arxiv updated 2018/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have nonnegative solutions. We then develop a monotone iterative method to find a nonnegative solution to an M-tensor equation. The method can be regarded as an approximation to Newton's method for solving the equation. At each iteration, we solve a system of linear equations. An advantage of the proposed method is that the coefficient matrices of the linear systems are independent of the iteration. We show that if the initial point is appropriately chosen, then the sequence of iterates generated by the method converges to a nonnegative solution of the M- tensor equation monotonically and linearly. At last, we do numerical experiments to test the proposed methods. The results show the efficiency of the proposed methods.