AN ULM-LIKE METHOD FOR SOLVING NONLINEAR OPERATOR EQUATIONS

被引：0

作者：

Shen, Wei-Ping ^{[1
]}

Wei, Ting-Ting ^{[1
]}

Peng, Li-Hui ^{[2
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

[2] Zhejiang Gongshang Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2015年 / 16卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Nonlinear equation; Ulm method; Lipschitz condition; NEWTONS METHOD; RIEMANNIAN-MANIFOLDS; INVERSE; CONVERGENCE; THEOREM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an Ulm-like method is proposed for solving nonlinear operator equations. This method has an advantage over other known methods since it avoids computing Jacobian matrices and solving Jacobian equations. Under some mild conditions, we prove that this Ulm-like method converges locally to the solution with R-convergence rate 2. Moreover, numerical tests are given in the last section demonstrating the effectiveness of this Ulm-like method.

引用

页码：1439 / 1447

页数：9

共 23 条

[1] [Anonymous], 1967, IZV AKAD NAUK EST SS
[2] GENERALIZED IMPLICIT FUNCTION THEOREMS WHEN THE DERIVATIVE HAS NO BOUNDED INVERSE
CRAVEN, BD
NASHED, MZ
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1982, 6 (04) : 375 - 387
[3] Newton's method on Riemannian manifolds: covariant alpha theory
Dedieu, JP
Priouret, P
Malajovich, G
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2003, 23 (03) : 395 - 419
[4] The Ulm method under mild differentiability conditions
Ezquerro, J. A.
Hernandez, M. A.
[J]. NUMERISCHE MATHEMATIK, 2008, 109 (02) : 193 - 207
[5] Kantorovich's theorem on Newton's method in Riemannian manifolds
Ferreira, OP
Svaiter, BF
[J]. JOURNAL OF COMPLEXITY, 2002, 18 (01) : 304 - 329
[6] The theory of Newton's method
Galántai, A
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 124 (1-2) : 25 - 44
[7] Ulm's method under regular smoothness
Galperin, A
Waksman, Z
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1998, 19 (3-4) : 285 - 307
[8] A note on a modification of Moser's method
Gutierrez, J. M.
Hernandez, M. A.
Romero, N.
[J]. JOURNAL OF COMPLEXITY, 2008, 24 (02) : 185 - 197
[9] Hald O. H., 1975, NUMER MATH, V23, P411
[10] AN ADAPTIVE NEWTON ALGORITHM BASED ON NUMERICAL INVERSION - REGULARIZATION AS POSTCONDITIONER
JEROME, JW
[J]. NUMERISCHE MATHEMATIK, 1985, 47 (01) : 123 - 138

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