A multivariate spectral projection method for solving nonlinear monotone equations

Abstract

ystems of nonlinear monotone equations have applications in many fields, such as engineering, economics, management science, probability theory, differential equations and other applied sciences. In this paper, a multivariate spectral projection method for solving nonlinear monotone problem is presented. The proposed method which combines a dirivative-free spectral algorithm and projection method is actually a multivariate version of the spectral algorithm. The method also can be regarded as a quasi-Newton type method that uses a non-scalar diagonal matrix as the approximation of the Jacobian matrix. Under the conditions that the nonlinear equations is monotone and Lipschitz continuous, we have shown that the method is globally convergent to a solution of the system. Numerical experiments are also given to show the method is efficient for nonlinear monotone problem