Adaptive Steffensen-like Methods with Memory for Solving Nonlinear Equations with the Highest Possible Efficiency Indices
Authors
Abstract:
The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous iteration. However, it is possible to improve the accelerators. Therefore, we achieve superior convergence orders and obtain as high efficiency indices as possible.
similar resources
A NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX
It is attempted to extend a two-step without memory method to it's with memory. Then, a new two-step derivative free class of without memory methods, requiring three function evaluations per step, is suggested by using a convenient weight function for solving nonlinear equations. Eventually, we obtain a new class of methods by employing a self-accelerating parameter calculated in each iterative...
full textTwo new three and four parametric with memory methods for solving nonlinear equations
In this study, based on the optimal free derivative without memory methods proposed by Cordero et al. [A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, Mathematical and Computer Modeling. 57 (2013) 1950-1956], we develop two new iterative with memory methods for solving a nonline...
full textInterpolatory multipoint methods with memory for solving nonlinear equations
A general way to construct multipoint methods for solving nonlinear equations by using inverse interpolation is presented. The proposed methods belong to the class of multipoint methods with memory. In particular, a new two-point method with memory with the order ð5þ ffiffiffiffiffiffi 17 p Þ=2 4:562 is derived. Computational efficiency of the presented methods is analyzed and their comparison ...
full textSolving Nonlinear Equations Using Steffensen-Type Methods With Optimal Order of Convergence
The author would like to express his deep gratitude to F. Soleymani for his comments which resulted in considerable improvement in the quality of this paper. Thus, he is much grateful for A.E.Alamir for his helpful hints and a great deal of patience in reviewing this paper. The author is also thankful to the reviewer for his constructive remarks and suggestions which have enhanced the present p...
full texttwo new three and four parametric with memory methods for solving nonlinear equations
in this study, based on the optimal free derivative without memory methods proposed by cordero et al. [a. cordero, j.l. hueso, e. martinez, j.r. torregrosa, generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, mathematical and computer modeling. 57 (2013) 1950-1956], we develop two new iterative with memory methods for solving a nonline...
full textA 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...
full textMy Resources
Journal title
volume 11 issue 4
pages 337- 345
publication date 2019-12-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023