New Parameters of the Conjugate Gradient Method to Solve Nonlinear Systems of Equations

Rana Z.  Al-Kawaz; Abbas Y.  Al-Bayati

doi:10.24996/ijs.2024.65.7.31

Authors

Rana Z. Al-Kawaz Department of Mathematics, College of Basic Education, University of Telafer, Mosul, Iraq 2University of Telafer, Mosul, Iraq
Abbas Y. Al-Bayati Department of Mathematics, College of Basic Education, University of Telafer, Mosul, Iraq 2University of Telafer, Mosul, Iraq

DOI:

https://doi.org/10.24996/ijs.2024.65.7.31

Keywords:

Conjugate gradient, Smooth functions, Projection technique, Free derivative methods

Abstract

The conjugated gradient methods can solve smooth functions with large-scale variables in the specified number of iterations for that they are highly important methods compared to concerning other iterative methods. In this paper, we propose two new conjugate gradient methods, namely the PMDL-1 and PMDL-2. However, for non-smooth functions, which are called conjugate gradient-free derivative methods depending on the projection technique. The two methods give great results compared to the basic PDL method. Moreover, we provide theorems that prove the global convergence between these two methods.