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

页码：577 / 594

页数：18

共 50 条

[21] Analysis Local Convergence of Gauss-Newton Method
Siregar, Rahmi Wahidah
Tulus
Ramli, Marwan
4TH INTERNATIONAL CONFERENCE ON OPERATIONAL RESEARCH (INTERIOR), 2018, 300
[22] Adaptive Gauss-Newton Method for Solving Systems of Nonlinear Equations
Yudin, N. E.
DOKLADY MATHEMATICS, 2021, 104 (02) : 293 - 296
[23] LOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD FOR INJECTIVE-OVERDETERMINED SYSTEMS
Amat, Sergio
Argyros, Ioannis Konstantinos
Alberto Magrenan, Angel
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 51 (05) : 955 - 970
[24] Improved local convergence of Newton's method under weak majorant condition
Argyros, Ioannis K.
Hilout, Said
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (07) : 1892 - 1902
[25] On convergence rates for the iteratively regularized Gauss-Newton method
Blaschke, B
Neubauer, A
Scherzer, O
IMA JOURNAL OF NUMERICAL ANALYSIS, 1997, 17 (03) : 421 - 436
[26] The Gauss-Newton method for finding singular solutions to systems of nonlinear equations
Yerina M.Yu.
Izmailov A.F.
Computational Mathematics and Mathematical Physics, 2007, 47 (5) : 748 - 759
[27] Convergence of Gauss-Newton's method and uniqueness of the solution
Chen, JH
Li, WG
APPLIED MATHEMATICS AND COMPUTATION, 2005, 170 (01) : 686 - 705
[28] On convergence of the Gauss-Newton method for convex composite optimization
Li, C
Wang, XH
MATHEMATICAL PROGRAMMING, 2002, 91 (02) : 349 - 356
[29] On convergence of the Gauss-Newton method for convex composite optimization
Chong Li
Xinghua Wang
Mathematical Programming, 2002, 91 : 349 - 356
[30] THE PROBLEM OF THE CONVERGENCE OF THE ITERATIVELY REGULARIZED GAUSS-NEWTON METHOD
BAKUSHINSKII, AB
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1992, 32 (09) : 1353 - 1359

← 1 2 3 4 5 →