BARZILAI-BORWEIN-LIKE METHOD FOR SOLVING LARGE-SCALE NON-LINEAR SYSTEMS OF EQUATIONS
Hassan Mohammad · Journal of the Nigerian Mathematical Society · 2017
In this paper, a derivative-free Barzilai-Borweinlike algorithm is developed for solving large-scale non-linear systems of equations. The algorithm is based on approximating the Jacobian matrix in quasi-Newton manner using a scalar multiple of an identity matrix. Under suitable conditions, we show that the proposed algorithm is locally superlinearly convergent. Numerical results show that the proposed method is efficient for large-scale problems (up to $10^6$) variables.