NEW SPECTRAL PARAMETER VIA SECANT CONDITION FOR SYMMETRIC NONLINEAR EQUATIONS

NEW SPECTRAL PARAMETER VIA SECANT CONDITION

Abstract

In this research, a New Spectral Parameter (NSP) is derived via Secant Condition with two-term direction and the classical Newton's direction using similar approach used to derive Conjugate Parameter by Waziri et al \cite{43}. The proposed method generates a descent direction using inexact line search and the global convergence of the proposed algorithm was established under appropriate conditions. The codes were written in MATLAB where iterations stop if the total number of iterations exceed 1000 or $\|F(x_{k})\|\leq10^{-4}$. The two methods were tested using five (5) test problems with different initial points and dimensions (n values). Numerical results for the benchmark test problems using the profile of Dolan and Mor$\acute{e}$ \cite{27}, which is a tool for evaluating and comparing the performance of iterative methods, shows that our proposed method is more efficient and effective than some existing ones in the literature.