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求解M-张量方程的两种新型算法

邵新慧, 祁猛   

  1. 东北大学理学院, 沈阳 110819
  • 收稿日期:2020-11-26 出版日期:2022-05-14 发布日期:2022-05-06
  • 基金资助:
    中央高校基本业务费(N2005013)资助.

邵新慧, 祁猛. 求解M-张量方程的两种新型算法[J]. 计算数学, 2022, 44(2): 206-216.

Shao Xinhui, Qi Meng. TWO NEW ALGORITHMS FOR SOLVING MULTI-LINEAR SYSTEMS WITH M-TENSOR[J]. Mathematica Numerica Sinica, 2022, 44(2): 206-216.

TWO NEW ALGORITHMS FOR SOLVING MULTI-LINEAR SYSTEMS WITH M-TENSOR

Shao Xinhui, Qi Meng   

  1. College of Science, Northeastern University, Shenyang 110819, China
  • Received:2020-11-26 Online:2022-05-14 Published:2022-05-06
多重线性系统在当今的工程计算和数据挖掘等领域有很多实际应用,许多问题可以转化为多重线性系统求解问题.在本文中,我们首先提出了一种新的迭代算法来求解系数张量为M-张量的多重线性系统,在此基础上又提出了一种新的改进算法,并对两种算法的收敛性进行了分析.数值算例的结果表明,本文提出的两种算法是有效的并且改进算法的迭代时间更少.
In engineering and science fields, some problems can be transformed into multi-linear system problems. We propose a new iteration algorithm to solve multi-linear systems with M-tensor. But this algorithm requires solving polynomial functions. For this reason, we give a simplified algorithm to improve. Then we give the convergence analysis of two algorithms. The results of numerical examples show that algorithms we propose are more effective.

MR(2010)主题分类: 

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