An iterative procedure for solving nonlinear equations

AN ITERATIVE METHOD WITH SIX-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

Modification of Newtons method with higher-order convergence is presented. The modification of Newtons method is based on Frontinis three-order method. The new method requires two-step per iteration. Analysis of convergence demonstrates that the order of convergence is 6. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and ...

An Iterative Scheme for Solving Nonlinear Equations with Monotone Operators

An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A discrete version of the Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with monotone operators is proposed and its convergence is proved. A discrepancy principle is proposed and justified. A priori and a posterior...

An acceleration of iterative processes for solving nonlinear equations

8 Abstract 9 The purpose of the paper is to present a method for acceleration of iterative proc-10 esses for solving a nonlinear equation. This approach is generalized for the case of mul-11 tiple roots when the multiplicity rate is preliminarily known. Thus some new methods 12 are obtained. The convergence analysis of the presented method and numerical exam-13 ples are given.

A Three-Point Iterative Method for Solving Nonlinear Equations with High Efficiency Index

In this paper, we proposed a three-point iterative method for finding the simple roots of non- linear equations via mid-point and interpolation approach. The method requires one evaluation of the derivative and three(3) functions evaluation with efficiency index of 81/4 ≈ 1.682. Numerical results reported here, between the proposed method with some other existing methods shows that our method i...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations