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.

Automated summary

Recent research on the multilinear system Axm-1=b with tensor A of order-m and dimension-n and vector b of dimension-n has focused on its applications in data mining, numerical PDEs, tensor complementary problems, etc. This paper introduces an alternating minimization method for solving this system and presents randomized versions to enhance performance, with numerical experiments demonstrating their superiority over existing methods in the same scenarios.