2018/11/25 by Xueli Bai, Bai, Xueli, Hongjin He +5 · 1 citation
Engineering · Mathematics · #15A18 #90C30 #90C33 #FOS: Mathematics #Optimization and Control (math.OC) #Power System Optimization and Stability #Tensor decomposition and applications #math.OC #msc:15A18 #msc:90C30 #msc:90C33
paper · pdf · doi:10.48550/arxiv.1811.09917
20 pages, three figures and 2 tables
openalex publication_date 2018/11/25 · arxiv created 2019/05/13 · arxiv updated 2019/05/14 · openalex created_date 2019/05/16 · openalex updated_date 2026/07/28
This paper addresses multilinear systems of equations which arise in various applications such as data mining and numerical partial differential equations. When the multilinear system under consideration involves a nonsingular M-tensor and a nonnegative right-hand side vector, it may have multiple nonnegative solutions. In this paper, we propose an algorithm which can always preserve the nonnegativity of solutions. Theoretically, we show that the sequence generated by the proposed algorithm is a nonnegative decreasing sequence and converges to a nonnegative solution of the system. Numerical results further support the novelty of the proposed method. Particularly, when some elements of the right-hand side vector are zeros, the proposed algorithm works well while existing state-of-the-art solvers may not produce a nonnegative solution.