A New Hybrid Approach for Solving Large-scale Monotone Nonlinear Equations

Jamilu Sabi'u (Department of Mathematics, Northwest University Kano)
Abdullah Shah (1Department of Mathematics, COMSATS University Islamabad)
Mohammed Yusuf Waziri (Department of Mathematical Sciences, Bayero University Kano)
Muhammad Kabir Dauda (Department of Mathematics and Statistics, Kaduna Polytechnic, Kaduna)

Journal of Mathematical and Fundamental Sciences
Vol. 52 No. 1 (2020)

In this paper, a new hybrid conjugate gradient method for solving monotone nonlinear equations is introduced. The scheme is a combination of the Fletcher-Reeves (FR) and Polak-Ribiére-Polyak (PRP) conjugate gradient methods with the Solodov and Svaiter projection strategy. Using suitable assumptions, the global convergence of the scheme with monotone line search is provided. Lastly, a numerical experiment was used to enumerate the suitability of the proposed scheme for large-scale problems.