A homotopy method for solving multilinear systems with M-tensors
A homotopy method for solving multilinear systems with M-tensors
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DOI：
10.1016/j.aml.2017.01.019
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发表时间：
2017-01
期刊：
影响因子：
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通讯作者：
Lixing Han
中科院分区：
文献类型：
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作者：
Lixing Han
多线性方程组有很多应用，如数值偏微分方程、数据挖掘和张量互补问题。本文提出了一种求具有非奇异m张量和正右向量的多线性系统的唯一正解的同伦方法。对该方法进行了分析，并证明了其收敛性。我们报告了一些数值结果，这些结果是基于使用路径跟踪的预测校正方法实现的。
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.