Alternating Minimization Methods for Solving Multilinear Systems

Recent works on the multilinear system Axm−1=b with an order-m and dimension-n tensor A and a vector b of dimension-n have been motivated by their applications in data mining, numerical PDEs, tensor complementary problems, and so on. In this paper, we propose an alternating minimization method for the solution of the system mentioned above and present several randomized versions of this algorithm in order to improve its performance. The provided numerical experiments show that our methods are feasible for any tensor A and outperform some existing ones in the same case.