A spectral algorithm for large-scale systems of nonlinear monotone equations

A derivative-free iterative scheme that uses the residual vector as search direction for solving large-scale systems of nonlinear monotone equations is presented. It is closely related to two recently proposed spectral residual methods for nonlinear systems which use a nonmonotone line-search globalization strategy and a step-size based on the Barzilai-Borwein choice. The global convergence analysis is presented. In order to study the numerical behavior of the algorithm, it is included an extensive series of numerical experiments. Our computational experiments show that the new algorithm is computationally efficient.