Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces

被引：8

作者：

Wang, Xiuhua ^{[1
]}

Kou, Jisheng ^{[1
]}

Gu, Chuanqing ^{[2
]}

机构：

[1] Xiaogan Univ, Sch Math & Stat, Xiaogan 432100, Hubei, Peoples R China

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

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2012年 / 153卷 / 03期

关键词：

Nonlinear equations in Banach spaces; Semilocal convergence; Recurrence relations; Super-Halley method; Iterative method; RATIONAL CUBIC METHODS; RECURRENCE RELATIONS; 4TH-ORDER CONVERGENCE;

D O I：

10.1007/s10957-012-9985-9

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we consider the semilocal convergence of a class of modified super-Halley methods for solving nonlinear equations in Banach spaces. The semilocal convergence of this class of methods is established by using recurrence relations. We construct a system of recurrence relations for the methods, and based on it, we prove an existence-uniqueness theorem that shows the -order of the methods.

引用

页码：779 / 793

页数：15

共 14 条

[1] RECURRENCE RELATIONS FOR RATIONAL CUBIC METHODS .1. THE HALLEY METHOD
CANDELA, V
MARQUINA, A
[J]. COMPUTING, 1990, 44 (02) : 169 - 184
[2] RECURRENCE RELATIONS FOR RATIONAL CUBIC METHODS .2. THE CHEBYSHEV METHOD
CANDELA, V
MARQUINA, A
[J]. COMPUTING, 1990, 45 (04) : 355 - 367
[3] Dawson C.N., 1997, Comput. Geosci., V1, P215, DOI [10.1023/A:1011521413158, DOI 10.1023/A:1011521413158]
[4] New iterations of R-order four with reduced computational cost
Ezquerro, J. A.
Hernandez, M. A.
[J]. BIT NUMERICAL MATHEMATICS, 2009, 49 (02) : 325 - 342
[5] Recurrence relations for Chebyshev-type methods
Ezquerro, JA
Hernández, MA
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2000, 41 (02) : 227 - 236
[6] An acceleration of Newton's method:: Super-Halley method
Gutiérrez, JM
Hernández, MA
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2001, 117 (2-3) : 223 - 239
[7] Recurrence relations for the super-Halley method
Gutierrez, JM
Hernandez, MA
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 36 (07) : 1 - 8
[8] Chebyshev's approximation algorithms and applications
Hernández, MA
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2001, 41 (3-4) : 433 - 445
[9] A family of modified super-Halley methods with fourth-order convergence
Kou, Jisheng
Li, Yitian
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 189 (01) : 366 - 370
[10] A variant of super-Halley method with accelerated fourth-order convergence
Kou, Jisheng
Li, Yitian
Wang, Xiuhua
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (01) : 535 - 539

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