scholarly journals Erratum: Ahmad, F., et al. A Preconditioned Iterative Method for Solving Systems of Nonlinear Equations Having Unknown Multiplicity. Algorithms 2017, 10, 17

Algorithms ◽  
2017 ◽  
Vol 10 (2) ◽  
pp. 55
Author(s):  
Fayyaz Ahmad ◽  
Toseef Bhutta ◽  
Umar Shoaib ◽  
Malik Ullah ◽  
Ali Alshomrani ◽  
...  
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Preconditioned Iterative

scholarly journals A Preconditioned Iterative Method for Solving Systems of Nonlinear Equations Having Unknown Multiplicity

Algorithms ◽  
2017 ◽  
Vol 10 (1) ◽  
pp. 17 ◽  
Author(s):  
Fayyaz Ahmad ◽  
Toseef Bhutta ◽  
Umar Shoaib ◽  
Malik Zaka Ullah ◽  
Ali Alshomrani ◽  
...  
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Preconditioned Iterative

scholarly journals On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Montazeri ◽  
F. Soleymani ◽  
S. Shateyi ◽  
S. S. Motsa
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
The Other ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Tests ◽  
Programming Package ◽  
New Iterative Method

We consider a system of nonlinear equationsF(x)=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

scholarly journals Frozen jacobian iterative method for solving systems of nonlinear equations application to nonlinear IVPs and BVPs

2016 ◽  
Vol 09 (12) ◽  
pp. 6021-6033 ◽  
Author(s):  
Malik Zaka Ullah ◽  
Fayyaz Ahmad ◽  
Ali Saleh Alshomrani ◽  
A. K. Alzahrani ◽  
Metib Said Alghamdi ◽  
...  
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations

scholarly journals Multi-Step Preconditioned Newton Methods for Solving Systems of Nonlinear Equations

2017 ◽  
Author(s):  
Fayyaz Ahmad ◽  
Malik Zaka Ullah ◽  
Ali Saleh Alshomrani ◽  
Shamshad Ahmad ◽  
Aisha M. Alqahtani ◽  
...  
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Numerical Stability ◽  
Order Of Convergence ◽  
Convergence Order ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Newton Methods ◽  
Rapid Convergence ◽  
Base Method

The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

Sign in / Sign up

Export Citation Format

Share Document