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.

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 Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Santiago Artidiello ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Iterative Methods ◽  
Order Of Convergence ◽  
Nonlinear Function ◽  
Nonlinear Problems ◽  
Basins Of Attraction ◽  
Weight Functions ◽  
Systems Of Nonlinear Equations ◽  
Functional Evaluation ◽  
Numerical Tests ◽  
High Order Iterative Methods

We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points.

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 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 High-Order Iterative Methods for the DMP Inverse

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Xiaoji Liu ◽  
Naping Cai
Keyword(s):  
Error Estimate ◽  
Iterative Methods ◽  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Sufficient Conditions For Convergence ◽  
Necessary And Sufficient ◽  
High Order Iterative Methods

We investigate two iterative methods for computing the DMP inverse. The necessary and sufficient conditions for convergence of our schemes are considered and the error estimate is also derived. Numerical examples are given to test the accuracy and effectiveness of our methods.

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