Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces

被引：1

作者：

Argyros, I. K. ^{[1
]}

Gonzalez, D. ^{[2
]}

Khattri, S. K. ^{[3
]}

机构：

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

[2] Univ Las Amer, Escuela Ciencias Fis & Matemat, Quito, Ecuador

[3] Stord Haugesund Univ Coll, Dept Engn, Haugesund, Norway

来源：

COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE | 2016年 / 57卷 / 03期

关键词：

Banach space; Newton's method; local convergence; radius of convergence;

D O I：

10.14712/1213-7243.2015.171

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a local convergence analysis of a one parameter Jarratt-type method. We use this method to approximate a solution of an equation in a Banach space setting. The semilocal convergence of this method was recently carried out in earlier studies under stronger hypotheses. Numerical examples are given where earlier results such as in [Ezquerro J.A., Hernandez M.A., New iterations of R-order four with reduced computational cost, BIT Numer. Math. 49 (2009), 325-342] cannot be used to solve equations but our results can be applied.

引用

页码：289 / 300

页数：12

共 22 条

[1] Adaptive approximation of nonlinear operators
Amat, S
Busquier, S
Negra, M
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2004, 25 (5-6) : 397 - 405
[2] Argyros I.K., 2013, COMPUTATIONAL METHOD
[3] Argyros IK, 2007, STUDIES COMPUTATIONA
[4] Estimating upper bounds on the limit points of majorizing sequences for Newton's method
Argyros, Ioannis K.
Hilout, Said
[J]. NUMERICAL ALGORITHMS, 2013, 62 (01) : 115 - 132
[5] Weaker conditions for the convergence of Newton's method
Argyros, Ioannis K.
Hilout, Said
[J]. JOURNAL OF COMPLEXITY, 2012, 28 (03) : 364 - 387
[6] Argyros IK, 2011, MATH COMPUT, V80, P327
[7] RECURRENCE RELATIONS FOR RATIONAL CUBIC METHODS .1. THE HALLEY METHOD
CANDELA, V
MARQUINA, A
[J]. COMPUTING, 1990, 44 (02) : 169 - 184
[8] RECURRENCE RELATIONS FOR RATIONAL CUBIC METHODS .2. THE CHEBYSHEV METHOD
CANDELA, V
MARQUINA, A
[J]. COMPUTING, 1990, 45 (04) : 355 - 367
[9] The inexact, inexact perturbed, and quasi-Newton methods are equivalent models
Catinas, E
[J]. MATHEMATICS OF COMPUTATION, 2005, 74 (249) : 291 - 301
[10] Third-order family of methods in Banach spaces
Chun, Changbum
Stanica, Pantelimon
Neta, Beny
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (06) : 1665 - 1675

← 1 2 3 →