Newton-type methods on Riemannian manifolds under Kantorovich-type conditions

被引：11

作者：

Amat, S. ^{[1
]}

Argyros, I. K. ^{[2
]}

Busquier, S. ^{[1
]}

Castro, R. ^{[3
]}

Hilout, S. ^{[4
,5
]}

Plaza, S. ^{[3
]}

机构：

[1] Univ Politecn Cartagena, Dpto Matemat Aplicada & Estadist, Cartagena, Spain

[2] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[3] Univ Valparaiso, Fac Ciencias, Dept Matemat, Valparaiso, Chile

[4] Univ Quebec Montreal, Dept Sci Terre & Atmosphere, Montreal, PQ H3C 3P8, Canada

[5] Univ Poitiers, Lab Math & Applicat, F-86962 Futuroscope, France

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 227卷

关键词：

Third-order iterative methods; Riemannian manifolds; Kantorovich conditions; Semilocal convergence; Order of convergence; SEMILOCAL CONVERGENCE ANALYSIS; BANACH-SPACES; RECURRENCE RELATIONS; R-ORDER; LEAST;

D O I：

10.1016/j.amc.2013.11.055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

One of the most studied problems in numerical analysis is the approximation of nonlinear equations using iterative methods. In the last years, attention has been paid in studying Newton's method on manifolds. In this paper, we generalize this study considering some Newton-type iterative methods. A characterization of the convergence under Kantorovich type conditions and optimal estimates of the error are found. Using normal coordinates the order of convergence is derived. The sufficient semilocal convergence criteria are weaker and the majorizing sequences are tighter for the special cases of simplified Newton and Newton methods than in earlier studies such as Argyros (2004, 2007, 2008) [6,8,12] and Kantorovich and Akilov (1964) [32]. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：762 / 787

页数：26

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