scholarly journals A trust region spectral method for large-scale systems of nonlinear equations

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Meilan Zeng ◽  
Guanghui Zhou
Keyword(s):  
Spectral Method ◽  
Nonlinear Equations ◽  
Large Scale ◽  
Trust Region ◽  
Systems Of Nonlinear Equations ◽  
Large Scale Systems

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 A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
M. Y. Waziri ◽  
W. J. Leong ◽  
M. Mamat
Keyword(s):  
Nonlinear Equations ◽  
Large Scale ◽  
Single Step ◽  
Secant Method ◽  
Diagonal Form ◽  
Systems Of Nonlinear Equations ◽  
Large Scale Systems ◽  
Secant Equation ◽  
Using Data ◽  
Matrix Free

We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance.

scholarly journals A Simple Three-term Conjugate Gradient Algorithm for Solving Symmetric Systems of Nonlinear Equations

2016 ◽  
Vol 5 (3) ◽  
pp. 118 ◽  
Author(s):  
M. Y. Waziri ◽  
L. Muhammad ◽  
J. Sabi’u
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Systems Of Nonlinear Equations ◽  
Large Scale Systems ◽  
Large Scale Problems ◽  
Derivative Free ◽  
Symmetric Systems

<p>This paper presents a simple three-terms Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear equations without computing Jacobian and gradient via the special structure of the underlying function. This three term CG of the proposed method has an advantage of solving relatively large-scale problems, with lower storage requirement compared to some existing methods. By incoporating the Powel restart approach in to the algorithm, we prove the global convergence of the proposed method with a derivative free line search under suitable assumtions. The numerical results are presented which show that the proposed method is promising.</p>

scholarly journals An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammed Yusuf Waziri ◽  
Zanariah Abdul Majid
Keyword(s):  
Nonlinear Equations ◽  
Large Scale ◽  
Systems Of Nonlinear Equations ◽  
Numerical Comparison ◽  
Large Scale Systems ◽  
Additional Information ◽  
Cauchy Relation ◽  
Diagonal Updating ◽  
Quasi Newton

We present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the performance of diagonal updating, by modifying the quasi-Cauchy relation so as to carry some additional information from the functions. The effectiveness of our proposed scheme is appraised through numerical comparison with some well-known Newton-like methods.

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