Abstract
In this paper, we consider a system of large-scale nonlinear monotone equations and propose a class of derivative-free spectral conjugate gradient methods to solve it efficiently. We demonstrate the appropriate analytical features of this class and prove the global convergence theorems under a backtracking line search technique. In order to illustrate the numerical effectiveness of our class, we organize a competition in which 405 test problems will be solved by some members of the new class and four other similar derivative-free conjugate gradient methods. All the analytical and numerical results indicate that the presented class is promising.
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