Third-order methods on Riemannian manifolds under Kantorovich conditions

被引：9

作者：

Amat, S. ^{[1
]}

Busquier, S. ^{[1
]}

Castro, R. ^{[2
]}

Plaza, S. ^{[2
]}

机构：

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

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

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 255卷

关键词：

Third-order iterative methods; Riemannian manifolds; Semi local convergence; NEWTONS METHOD; QUADRATIC EQUATIONS; GAMMA-CONDITION; R-ORDER; LEAST; CONVERGENCE; ITERATION;

D O I：

10.1016/j.cam.2013.04.023

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 past years, attention has been paid in studying Newton's method on manifolds. In this paper, we generalize this study by considering a general class of third-order iterative methods. A characterization of the convergence under Kantorovich type conditions and optimal error estimates is found. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：106 / 121

页数：16

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