Improved conjugate gradient method for nonlinear system of equations

2020 ◽  
Vol 39 (4) ◽  
Author(s):  
Mohammed Yusuf Waziri ◽  
Aliyu Yusuf ◽  
Auwal Bala Abubakar
Keyword(s):  
Nonlinear System ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
System Of Equations ◽  
Nonlinear System Of Equations

scholarly journals An Alternative Modified Conjugate Gradient Coefficient for Solving Nonlinear System of Equations

2019 ◽  
Vol 2 (3) ◽  
pp. 5-8
Author(s):  
Muhammad Kabir Dauda ◽  
Shehu Usman ◽  
Hayatu Ubale ◽  
M Mamat
Keyword(s):  
Nonlinear System ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Real Life ◽  
Computational Method ◽  
Benchmark Problems ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Sufficient Descent Condition

In mathematical term, the method of solving models and finding the best alternatives is known as optimization. Conjugate gradient (CG) method is an evolution of computational method in solving optimization problems. In this article, an alternative modified conjugate gradient coefficient for solving large-scale nonlinear system of equations is presented. The method is an improved version of the Rivaie et el conjugate gradient method for unconstrained optimization problems. The new CG is tested on a set of test functions under exact line search. The approach is easy to implement due to its derivative-free nature and has been proven to be effective in solving real-life application. Under some mild assumptions, the global convergence of the proposed method is established. The new CG coefficient also retains the sufficient descent condition. The performance of the new method is compared to the well-known previous PRP CG methods based on number of iterations and CPU time. Numerical results using some benchmark problems show that the proposed method is promising and has the best efficiency amongst all the methods tested.

scholarly journals Analyzing the Effect of Local Rounding Error Propagation on the Maximal Attainable Accuracy of the Pipelined Conjugate Gradient Method

2018 ◽  
Vol 39 (1) ◽  
pp. 426-450 ◽  
Author(s):  
Siegfried Cools ◽  
Emrullah Fatih Yetkin ◽  
Emmanuel Agullo ◽  
Luc Giraud ◽  
Wim Vanroose
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Error Propagation ◽  
Rounding Error
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