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∈Rn, 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 Hoy's method. The Q-quadratic convergence of this algorithm and some numerical examples are given as well.