Double direction three-term spectral conjugate gradient method for solving symmetric nonlinear equations

Abstract

We propose a new three-term spectral conjugate gradient method via double direction approach by considering the first direction to be the one proposed by Halilu and Waziri (2018) and the other obtained by extending the direction proposed by Birgin and Mertinez (2001) to three-term spectral conjugate gradient (CG) direction. The propose method generates a descent direction via an inexact line search. The global convergence of the propose algorithm was established under appropriate conditions and numerical experiments on some benchmark test problems demonstrate its efficiency over some existing ones.

Keywords

• Double direction
• Spectral conjugate gradient method
• Secant condition
• Descent condition
• Global convergence