INEXACT NEWTON METHOD FOR M-TENSOR EQUATIONS

被引：0

作者：

Li, Dong-Hui ^{[1
]}

Guan, Hong-Bo ^{[1
,2
]}

Xu, Jie-Feng ^{[1
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

[2] Hunan Inst Technol, Sch Math Sci & Energy Engn, Hengyang 421002, Peoples R China

来源：

PACIFIC JOURNAL OF OPTIMIZATION | 2021年 / 17卷 / 04期

关键词：

M-tensor equation; inexact Newton method; global convergence; quadratic convergence; SOLVING MULTILINEAR SYSTEMS; NONNEGATIVE SOLUTION; ALGORITHM;

D O I：

暂无

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We first investigate properties of M-tensor equations. In particular, we show that if the constant term of the equation is nonnegative, then finding a nonnegative solution of the equation can be done by finding a positive solution of a lower dimensional M-tensor equation. We then propose an inexact Newton method to find a positive solution to the lower dimensional equation and establish its global convergence. We also show that the convergence rate of the method is quadratic. At last, we do numerical experiments to test the proposed Newton method. The results show that the proposed Newton method has a very good numerical performance.

引用

页码：617 / 643

页数：27

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