An efficient derivative free family of fourth order methods for solving systems of nonlinear equations

2014 ◽  
Vol 235 ◽  
pp. 383-393 ◽  
Author(s):  
Janak Raj Sharma ◽  
Himani Arora ◽  
Miodrag S. Petković
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Systems Of Nonlinear Equations ◽  
Derivative Free

An efficient fourth order weighted-Newton method for systems of nonlinear equations

2012 ◽  
Vol 62 (2) ◽  
pp. 307-323 ◽  
Author(s):  
Janak Raj Sharma ◽  
Rangan Kumar Guha ◽  
Rajni Sharma
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Fourth Order ◽  
Systems Of Nonlinear Equations

scholarly journals A Derivative-Free Decent Method Via Acceleration Parameter for Solving Systems of Nonlinear Equations

2019 ◽  
Vol 2 (3) ◽  
pp. 1-4
Author(s):  
Abubakar Sani Halilu ◽  
M K Dauda ◽  
M Y Waziri ◽  
M Mamat
Keyword(s):  
Nonlinear Equations ◽  
Large Scale ◽  
Line Search ◽  
Main Idea ◽  
Step Length ◽  
Descent Method ◽  
Systems Of Nonlinear Equations ◽  
Inexact Line Search ◽  
Large Scale Systems ◽  
Derivative Free

An algorithm for solving large-scale systems of nonlinear equations based on the transformation of the Newton method with the line search into a derivative-free descent method is introduced. Main idea used in the algorithm construction is to approximate the Jacobian by an appropriate diagonal matrix. Furthermore, the step length is calculated using inexact line search procedure. Under appropriate conditions, the proposed method is proved to be globally convergent under mild conditions. The numerical results presented show the efficiency of the proposed method.

scholarly journals Hybrid conjugate gradient parameter for solving symmetric systems of nonlinear equations

2019 ◽  
Vol 16 (1) ◽  
pp. 539
Author(s):  
M. K. Dauda ◽  
Mustafa Mamat ◽  
Mohamad A. Mohamed ◽  
Nor Shamsidah Amir Hamzah
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Numerical Solutions ◽  
Graphical Representation ◽  
Systems Of Nonlinear Equations ◽  
Inexact Line Search ◽  
Derivative Free ◽  
Gradient Parameter ◽  
The Given ◽  
Symmetric Systems

Mathematical models from recent research are mostly nonlinear equations in nature. Numerical solutions to such systems are widely needed and applied in those areas of  mathematics. Although, in recent years, this field received serious attentions and new approach were discovered, but yet the efficiency of the previous versions suffers setback. This article gives a new hybrid conjugate gradient parameter, the method is derivative-free and analyzed with an effective inexact line search in a given conditions. Theoretical proofs show that the proposed method retains the sufficient descent and global convergence properties of the original CG methods. The proposed method is tested on a set of test functions, then compared to the two previous classical CG-parameter that resulted the given method, and its performance is given based on number of iterations and CPU time. The numerical results show that the new proposed method is efficient and effective amongst all the methods tested. The graphical representation of the result justify our findings. The computational result indicates that the new hybrid conjugate gradient parameter is suitable and capable for solving symmetric systems of nonlinear equations.

Sign in / Sign up

Export Citation Format

Share Document