f Arzani - Faculty of Mathematics, K.N. Toosi University of Technology, P.O.Box ۱۶۳۱۵-۱۶۱۸, Tehran, Iran. Scientific Computations in OPtimization and Systems En- gineering (SCOPE), K.N. Toosi University of Technology, Tehran, Iran
m.r Peyghami - Faculty of Mathematics, K.N. Toosi University of Technology, P.O.Box ۱۶۳۱۵-۱۶۱۸, Tehran, Iran. Scientific Computations in OPtimization and Systems En-gineering (SCOPE), K.N. Toosi University of Technology, Tehran, Iran

In this paper, we present a new derivative—free spectral residual method for solving large—scale systems of equations. Our algorithm is equipped with a dwindling multidimensional nonmonotone filter in which whose envelope is dwindling as the step—length of line search is decreasing. The proposed algorithm is also combined with a relaxed nonmonotone line search technique which allows the algorithm to enjoy the nonmonotone property from scratch. Under some standard assumptions, the global convergence property of the proposed algorithm is established. Numerical results on some test problems show the efiiciency and effectiveness of the new algorithm in practice.

Dwindling filter technique; Systems of equations; Nonmonotone line search; Global convergence