A homotopy method for solving multilinear systems with M-tensors

被引：80
作者：
Han, Lixing [1 ]
机构：
[1] Univ Michigan Flint, Dept Math, Flint, MI 48502 USA
来源：
APPLIED MATHEMATICS LETTERS | 2017年 / 69卷
关键词：
M-tensor; Multilinear system; Homotopy method;
D O I：
10.1016/j.aml.2017.01.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Multilinear systems of equations arise in various applications, such as numerical partial differential equations, data mining, and tensor complementarity problems. In this paper, we propose a homotopy method for finding the unique positive solution to a multilinear system with a nonsingular M-tensor and a positive right side vector. We analyze the method and prove its convergence to the desired solution. We report some numerical results based on an implementation of the proposed method using a prediction-correction approach for path following. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：49 / 54
页数：6
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