Interval tensors and their application in solving multi-linear systems of equations

Inexact Newton Method for M-Tensor Equations

“…In this section, we list the detailed numerical results of the proposed methods compared with QCA method. The results are listed in Tables 3,4,5,6,7,8,9,10,11 and 12, where the columns 'Iter', 'Time', 'Res' and 'Ls-iter' stand for the total number of iterations, the computational time (in second) used for the method, the residual Âx From the data in the Tables 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12, we can see that the proposed methods are effective for all test problems. In terms of the number of iterations and CPU time, Inexact Newton method and Regularized Newton method are better than QCA method, and the number of linear search of the Regularized Newton method are far less than that of the QCA method.…”

“…There are also a few methods that can solve M-Teq (1.1) without restriction b ∈ R n ++ or that A is an M tensor. Those methods include the splitting method by Li, Guan and Wang [18], and Li, Xie and Xu [15], the alternating projection method by Li, Dai and Gao [17], the alternating iterative methods by Liang, Zheng and Zhao [23] etc.. Related works can also be found in [4,5,16,24,29,30,31,32,33,34].…”

On rank decomposition and semi-symmetric rank decomposition of semi-symmetric tensors

“…While tensors have been in use from the early 20th century [16], the interest in tensors in the recent decade has increased significantly and tensors are applied in many different fields [21,20,5,15,2,3]. This increasing interest is partly due to the fact that there exists a rising demand for modeling and solving more complicated problems and the fact that the computing power of computers has risen significantly in the recent decade.…”