scholarly journals On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Taher Lotfi ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
Morteza Amir Abadi ◽  
Maryam Mohammadi Zadeh
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Convergence ◽  
Eighth Order ◽  
Optimal Methods ◽  
Kung And Traub’S Conjecture

The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub’s conjecture relevant to construction optimal methods without memory. Moreover, some concrete methods of this class are shown and implemented numerically, showing their applicability and efficiency.

scholarly journals On Some Iterative Methods with Memory and High Efficiency Index for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Tahereh Eftekhari
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
High Efficiency ◽  
Efficiency Index ◽  
Order Convergence ◽  
Eighth Order ◽  
Additional Function ◽  
Numerical Comparisons ◽  
With Memory

Based on iterative methods without memory of eighth-order convergence proposed by Thukral (2012), some iterative methods with memory and high efficiency index are presented. We show that the order of convergence is increased without any additional function evaluations. Numerical comparisons are made to show the performance of the presented methods.

scholarly journals Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Gustavo Fernández-Torres ◽  
Juan Vásquez-Aquino
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
Classical Method ◽  
Multiple Roots ◽  
Order Convergence ◽  
Numerical Examples ◽  
Optimal Methods

We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to Kung-Traub's conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourth-order convergence recently published.

scholarly journals A Family of Iterative Methods with Accelerated Eighth-Order Convergence

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Alicia Cordero ◽  
Mojtaba Fardi ◽  
Mehdi Ghasemi ◽  
Juan R. Torregrosa
Keyword(s):  
Weight Function ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Function Method ◽  
Order Convergence ◽  
Eighth Order ◽  
Weight Function Method ◽  
Theoretical Results

We propose a family of eighth-order iterative methods without memory for solving nonlinear equations. The new iterative methods are developed by using weight function method and using an approximation for the last derivative, which reduces the required number of functional evaluations per step. Their efficiency indices are all found to be 1.682. Several examples allow us to compare our algorithms with known ones and confirm the theoretical results.

Numerical solution of nonlinear equations by an optimal eighth-order class of iterative methods

2012 ◽  
Vol 59 (1) ◽  
pp. 159-171 ◽  
Author(s):  
Fazlollah Soleymani ◽  
S. Karimi Vanani ◽  
Hani I. Siyyam ◽  
I. A. Al-Subaihi
Keyword(s):  
Numerical Solution ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Eighth Order
Sign in / Sign up

Export Citation Format

Share Document