Open AccessAlternating Minimization Methods for Solving Multilinear Systems
Author(s) -
Maolin Liang,
Li Dai
Publication year - 2021
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2021/6629243
Subject(s) - multilinear map , dimension (graph theory) , tensor (intrinsic definition) , minification , order (exchange) , mathematics , algebra over a field , algorithm , discrete mathematics , combinatorics , pure mathematics , mathematical optimization , finance , economics
Recent works on the multilinear system A x m − 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.