scholarly journals On a Family of High-Order Iterative Methods under Kantorovich Conditions and Some Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
S. Amat ◽  
C. Bermúdez ◽  
S. Busquier ◽  
M. J. Legaz ◽  
S. Plaza
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
High Order ◽  
High Order Iterative Methods

This paper is devoted to the study of a class of high-order iterative methods for nonlinear equations on Banach spaces. An analysis of the convergence under Kantorovich-type conditions is proposed. Some numerical experiments, where the analyzed methods present better behavior than some classical schemes, are presented. These applications include the approximation of some quadratic and integral equations.

scholarly journals A class of efficient high‐order iterative methods with memory for nonlinear equations and their dynamics

2018 ◽  
Vol 41 (17) ◽  
pp. 7263-7282 ◽  
Author(s):  
Cory L. Howk ◽  
José L. Hueso ◽  
Eulalia Martínez ◽  
Carles Teruel
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
High Order ◽  
With Memory ◽  
High Order Iterative Methods

scholarly journals Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Isaac Fried
Keyword(s):  
Iterative Methods ◽  
Asymptotic Form ◽  
Nonlinear Function ◽  
High Order ◽  
High Order Methods ◽  
High Order Iterative Methods

The asymptotic form of the Taylor-Lagrange remainder is used to derive some new, efficient, high-order methods to iteratively locate the root, simple or multiple, of a nonlinear function. Also derived are superquadratic methods that converge contrarily and superlinear and supercubic methods that converge alternatingly, enabling us not only to approach, but also to bracket the root.

scholarly journals HIGH-ORDER ITERATIVE METHODS FOR A NONLINEAR KIRCHHOFF WAVE EQUATION

2010 ◽  
Vol 43 (3) ◽  
Author(s):  
Le Thi Phuong Ngoc ◽  
Le Xuan Truong ◽  
Nguyen Thanh Long
Keyword(s):  
Wave Equation ◽  
Iterative Methods ◽  
High Order ◽  
High Order Iterative Methods

scholarly journals High order iterative methods for matrix inversion and regularized solution of fredholm integral equation of first kind with noisy data

2018 ◽  
Vol 22 ◽  
pp. 01002
Author(s):  
Suzan Cival Buranay ◽  
Ovgu Cidar Iyikal
Keyword(s):  
Integral Equation ◽  
Iterative Methods ◽  
Fredholm Integral Equation ◽  
Recurrence Formula ◽  
Noisy Data ◽  
Matrix Inversion ◽  
High Order ◽  
The Given ◽  
High Order Iterative Methods ◽  
Regularized Solution

The motivation of the present work is to propose high order iterative methods with a recurrence formula for approximate matrix inversion and provide regularized solution of Fredholm integral equation of first kind with noisy data by an algorithm using the proposed methods. From the given family of methods of orders p = 7,11,15,19 are applied to solve problems of Fredholm integral equation of first kind. From the literature, iterative methods of same orders are used to solve the considered problems and numerical comparisons are shown through tables and figures.

On a new family of high-order iterative methods for the matrix p th root

2015 ◽  
Vol 22 (4) ◽  
pp. 585-595 ◽  
Author(s):  
S. Amat ◽  
J. A. Ezquerro ◽  
M. A. Hernández-Verón
Keyword(s):  
Iterative Methods ◽  
High Order ◽  
New Family ◽  
The Matrix ◽  
High Order Iterative Methods

scholarly journals A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Young Ik Kim ◽  
Young Hee Geum
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Harmonic Mean ◽  
Optimal Order ◽  
Multiple Roots ◽  
Multiple Zeros ◽  
Asymptotic Error ◽  
Two Parameter

We develop a family of fourth-order iterative methods using the weighted harmonic mean of two derivative functions to compute approximate multiple roots of nonlinear equations. They are proved to be optimally convergent in the sense of Kung-Traub’s optimal order. Numerical experiments for various test equations confirm well the validity of convergence and asymptotic error constants for the developed methods.

scholarly journals Extended Semilocal Convergence for the Newton- Kurchatov Method

2020 ◽  
Vol 53 (1) ◽  
pp. 85-91
Author(s):  
H.P. Yarmola ◽  
I. K. Argyros ◽  
S.M. Shakhno
Keyword(s):  
Iterative Methods ◽  
Error Estimates ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Semilocal Convergence ◽  
Convergence Criteria ◽  
Precise Location ◽  
Lipschitz Constants ◽  
Restricted Region

We provide a semilocal analysis of the Newton-Kurchatov method for solving nonlinear equations involving a splitting of an operator. Iterative methods have a limited restricted region in general. A convergence of this method is presented under classical Lipschitz conditions.The novelty of our paper lies in the fact that we obtain weaker sufficient semilocal convergence criteria and tighter error estimates than in earlier works. We find a more precise location than before where the iterates lie resulting to at least as small Lipschitz constants. Moreover, no additional computations are needed than before. Finally, we give results of numerical experiments.

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