A modified Brown algorithm for solving singular nonlinear systems with rank defects

A modified Brown algorithm for solving a class of singular nonlinear systems, F ( x ) = 0 , where x , F ∈ R n , is presented. This method is constructed by combining the discreted Brown algorithm with the space transforming method. The second-order information of F ( x ) at a point is not required calculating, which is different from the tensor method and the Hoyʹs method. The Q -quadratic convergence of this algorithm and some numerical examples are given as well.