In this paper, we propose a family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations. They come from two modified conjugate gradient methods [W.Y. Cheng, A two term PRP based descent Method, Numer. Funct. Anal. Optim. 28 (2007) 1217-1230; L. Zhang, W.J. Zhou, D.H. Li, A descent modified Polak-Ribiére-Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal. 26 (2006) 629-640] recently proposed for unconstrained optimization problems. Under appropriate conditions, the global convergence of the proposed method is established. Preliminary numerical results show that the proposed method is promising. © 2008 Elsevier B.V. All rights reserved.
Cheng, W., Xiao, Y., & Hu, Q. J. (2009). A family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations. Journal of Computational and Applied Mathematics, 224(1), 11–19. https://doi.org/10.1016/j.cam.2008.03.050