Local convergence of Newton's method in Banach space from the viewpoint of the majorant principle

被引：31

作者：

Ferreira, Orizon P. ^{[1
]}

机构：

[1] Univ Fed Goias, Inst Math & Estat, BR-74001970 Goiania, Go, Brazil

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2009年 / 29卷 / 03期

关键词：

Newton's method; majorant principle; local convergence; Banach space; RIEMANNIAN-MANIFOLDS; EQUATIONS;

D O I：

10.1093/imanum/drn036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A local convergence analysis of Newton's method for solving nonlinear equations, based on Kantorovich's majorant principle, is presented in this paper. This analysis provides a clear relationship between the majorant function, which relaxes the Lipschitz continuity of the derivative, and the nonlinear operator under consideration. It also allows us to obtain the optimal convergence radius, the biggest range for the uniqueness of the solution, and to unify some previous and unrelated results.

引用

页码：746 / 759

页数：14

共 50 条

[1] Local convergence of Newton's method under majorant condition
Ferreira, O. P.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (05) : 1515 - 1522
[2] Unifying semilocal and local convergence of Newton's method on Banach space with a convergence structure
Argyros, Ioannis K.
Behl, Ramandeep
Motsa, S. S.
[J]. APPLIED NUMERICAL MATHEMATICS, 2017, 115 : 225 - 234
[3] On local convergence of a Newton-type method in Banach space
Argyros, Ioannis K.
Chen, Jinhai
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2009, 86 (08) : 1366 - 1374
[4] Improved local convergence of Newton's method under weak majorant condition
Argyros, Ioannis K.
Hilout, Said
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (07) : 1892 - 1902
[5] Local convergence of Newton's method under a majorant condition in Riemannian manifolds
Ferreira, Orizon P.
Silva, Roberto C. M.
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2012, 32 (04) : 1696 - 1713
[6] The majorant method and convergence for solving nondifferentiable equations in Banach space
Han, DF
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2001, 118 (01) : 73 - 82
[7] Convergence of Newton's method and inverse function theorem in Banach space
Wang, XH
[J]. MATHEMATICS OF COMPUTATION, 1999, 68 (225) : 169 - 186
[8] Convergence of Newton's method and uniqueness of the solution of equations in Banach space
Wang, XH
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2000, 20 (01) : 123 - 134
[9] Ball convergence of the Newton–Gauss method in Banach space
Argyros I.K.
Sharma J.R.
Kumar D.
[J]. SeMA Journal, 2017, 74 (4) : 429 - 439
[10] Local convergence analysis of the Gauss-Newton method under a majorant condition
Ferreira, O. P.
Goncalves, M. L. N.
Oliveira, P. R.
[J]. JOURNAL OF COMPLEXITY, 2011, 27 (01) : 111 - 125

← 1 2 3 4 5 →