A modified Newton method for solving non-symmetric algebraic Riccati equations arising in transport theory

被引：18

作者：

Lin, Yiqin ^{[3
]}

Bao, Liang ^{[4
]}

Wei, Yimin ^{[1
,2
]}

机构：

[1] Fudan Univ, Inst Math, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Fudan Univ, Minist Educ, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China

[3] Hunan Univ Sci & Engn, Dept Math & Computat Sci, Yongzhou 425006, Peoples R China

[4] E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2008年 / 28卷 / 02期

基金：

中国国家自然科学基金;

关键词：

non-symmetric algebraic Riccati equation; transport theory; minimal positive solution; M-matrix; modified Newton method;

D O I：

10.1093/imanum/drm010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The non-symmetric algebraic Riccati equation arising in transport theory can be rewritten as a vector equation and the minimal positive solution of the non-symmetric algebraic Riccati equation can be obtained by solving the vector equation. In this paper, we apply the modified Newton method to solve the vector equation. Some convergence results are presented. Numerical tests show that the modified Newton method is feasible and effective, and outperforms the Newton method.

引用

页码：215 / 224

页数：10

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