Fourth-order convergence theorem by using majorizing functions for super-Halley method in Banach spaces

被引：4

作者：

Zheng, Lin ^{[1
]}

Gu, Chuanqing ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2013年 / 90卷 / 02期

关键词：

nonlinear equations in Banach spaces; super-Halley method; majorizing functions; semilocal convergence; NewtonKantorovich theorem; 65J15; 65H10; 65G99; 47J25; 49M15; RATIONAL CUBIC METHODS; RECURRENCE RELATIONS; SEMILOCAL CONVERGENCE; NEWTON-KANTOROVICH; FAMILY; VARIANT;

D O I：

10.1080/00207160.2012.719608

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the semilocal convergence of a multipoint fourth-order super-Halley method for solving nonlinear equations in Banach spaces. We establish the NewtonKantorovich-type convergence theorem for the method by using majorizing functions. We also get the error estimate. In comparison with the results obtained in Wang et al. [X.H. Wang, C.Q. Gu, and J.S. Kou, Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces, Numer. Algorithms 56 (2011), pp. 497516], we can provide a larger convergence radius. Finally, we report some numerical applications to demonstrate our approach.

引用

页码：423 / 434

页数：12

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