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.
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机译：最近关于具有 m 阶和 n 维张量 A 和 n 维向量 b 的多线性系统 Axm-1=b 的研究，其在数据挖掘、数值偏微分方程、张量互补问题等方面的应用激发了它们的发展。为了提高该算法的性能，本文提出了一种交替最小化方法，并提出了该算法的几个随机版本。数值实验表明，该方法适用于任何张量A，并且在同一情况下优于现有的一些张量A。
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