Open AccessA Simple Three-term Conjugate Gradient Algorithm for Solving Symmetric Systems of Nonlinear Equations
Author(s) -
Lawal Muhammad,
Mohammed Yusuf Waziri,
Jamilu Sabi’u
Publication year - 2016
Publication title -
international journal of advances in applied sciences
Language(s) - English
Resource type - Journals
eISSN - 2722-2594
pISSN - 2252-8814
DOI - 10.11591/ijaas.v5.i3.pp118-127
Subject(s) - conjugate gradient method , nonlinear conjugate gradient method , jacobian matrix and determinant , convergence (economics) , term (time) , nonlinear system , simple (philosophy) , mathematics , line search , algorithm , scale (ratio) , derivative (finance) , gradient method , function (biology) , line (geometry) , mathematical optimization , computer science , gradient descent , geometry , artificial neural network , artificial intelligence , philosophy , computer security , economic growth , financial economics , biology , epistemology , quantum mechanics , evolutionary biology , economics , physics , radius
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.