Convergence of the Gauss-Newton method for a special class of systems of equations under a majorant condition

被引：6
作者：
Goncalves, M. L. N. [1 ]
Oliveira, P. R. [2 ]
机构：
[1] IME UFG, Goiania, Go, Brazil
[2] Univ Fed Rio de Janeiro, COPPE Sistemas, Rio De Janeiro, Brazil
来源：
OPTIMIZATION | 2015年 / 64卷 / 03期
关键词：
Gauss-Newton method; majorant condition; semi-local convergence; non-linear systems of equations; CONSTANT RANK DERIVATIVES; LOCAL CONVERGENCE; BANACH-SPACE; PRINCIPLE;
D O I：
10.1080/02331934.2013.778854
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：
In this paper, we study the Gauss-Newton method for a special class of systems of non-linear equation. On the hypothesis that the derivative of the function under consideration satisfies a majorant condition, semi-local convergence analysis is presented. In this analysis, the conditions and proof of convergence are simplified by using a simple majorant condition to define regions where the Gauss-Newton sequence is 'well behaved'. Moreover, special cases of the general theory are presented as applications.
引用
收藏
页码：577 / 594
页数：18
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