LOCAL CONVERGENCE FOR SOME THIRD-ORDER ITERATIVE METHODS UNDER WEAK CONDITIONS

被引：22

作者：

Argyros, Ioannis K. ^{[1
]}

Cho, Yeol Je ^{[2
,3
,4
]}

George, Santhosh ^{[5
]}

机构：

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

[2] Gyeongsang Natl Univ, Dept Math Educ, Jinju 660701, South Korea

[3] Gyeongsang Natl Univ, RINS, Jinju 660701, South Korea

[4] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

[5] NIT Karnataka, Dept Math & Computat Sci, Mangaluru 575025, Karnataka, India

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2016年 / 53卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

Newton method; order of convergence; local convergence; NEWTONS METHOD; SEMILOCAL CONVERGENCE; RECURRENCE RELATIONS; R-ORDER; VARIANT;

D O I：

10.4134/JKMS.j150244

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

引用

页码：781 / 793

页数：13

共 50 条

[41] On a Family of High-Order Iterative Methods under Kantorovich Conditions and Some Applications [J].

Amat, S. ;

Bermudez, C. ;

Busquier, S. ;

Legaz, M. J. ;

Plaza, S. .

ABSTRACT AND APPLIED ANALYSIS, 2012,

[42] On Global Convergence of Third-Order Chebyshev-Type Method under General Continuity Conditions [J].

Mallawi, Fouad Othman ;

Behl, Ramandeep ;

Maroju, Prashanth .

FRACTAL AND FRACTIONAL, 2022, 6 (01)

[43] A third-order iterative algorithm for inversion of cumulative central beta distribution [J].

Prabhu, K. Dhivya ;

Singh, Sanjeev ;

Vijesh, V. Antony .

NUMERICAL ALGORITHMS, 2023, 94 (03) :1331-1353

[44] New Families of Third-Order Iterative Methods for Finding Multiple Roots [J].

Lin, R. F. ;

Ren, H. M. ;

Smarda, Z. ;

Wu, Q. B. ;

Khan, Y. ;

Hu, J. L. .

JOURNAL OF APPLIED MATHEMATICS, 2014,

[45] Third-order iterative methods without using any Frechet derivative [J].

Amat, S ;

Busquier, S ;

Candela, V .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 158 (01) :11-18

[46] Local convergence for an almost sixth order method for solving equations under weak conditions [J].

Argyros I.K. ;

George S. .

SeMA Journal, 2018, 75 (2) :163-171

[47] ON THE R-ORDER CONVERGENCE OF A THIRD ORDER METHOD IN BANACH SPACES UNDER MILD DIFFERENTIABILITY CONDITIONS [J].

Parida, P. K. ;

Gupta, D. K. .

INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2009, 6 (02) :291-306

[48] Local convergence of a family of iterative methods for Hammerstein equations [J].

Martinez, Eulalia ;

Singh, Sukhjit ;

Hueso, Jose L. ;

Gupta, Dharmendra K. .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2016, 54 (07) :1370-1386

[49] Ball convergence of a sixth order iterative method with one parameter for solving equations under weak conditions [J].

Argyros, Ioannis K. ;

George, Santhosh .

CALCOLO, 2016, 53 (04) :585-595

[50] Ball convergence of a sixth order iterative method with one parameter for solving equations under weak conditions [J].

Ioannis K. Argyros ;

Santhosh George .

Calcolo, 2016, 53 :585-595

← 1 2 3 4 5 →