A combined (CG) method to solve nonlinear systems of equations

Habib, Hussein Saad; Shiker, Mushtak A. K.

doi:10.47974/JIM-1971

Open Access Research Article

A combined (CG) method to solve nonlinear systems of equations

^*Hussein Saad HabibCorresponding authorpure304.hussien.saad@student.uobabylon.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonHilla, Babylon, IraqView full profile → , Mushtak A. K. Shikerpure.mushtaq@uobabylon.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonHilla, Babylon, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 763–769Vol. 28Issue 3-AApril 2025DOI: 10.47974/JIM-1971XML

Received:: 07 May 2024
Published Online:: 08 May 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-1971
Pages:: 763–769

Abstract

In this work, a new conjugate gradient (CG) algorithm named the (H.M.) algorithm is presented as a combination of the search direction and the line search technique for solving nonlinear systems of unconstrained optimization problems. The main goal is to minimize the CPU time (NT2), the iterations number (Ni2) and the function evaluation number (Nf2) of the (H.M.) algorithm this is done through the program MATLAB (with version R2020a) and a numerical results comparison with two methods, (BFGS) and (BMLV) algorithm. Under some criterion circumstances, the well-defined and the convergence of the (H.M.) algorithm are proved, then taking introduction and proceeding to our aim.

Keywords

Nonlinear systems CGM Global convergence

Subject Classifications

46N1047N1090C30

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