Before revision:  with comparison to the traditional trust-region method (the built-in subroutine fsolve.m of the MATLAB environment \mbox{%DIFAUXCMD MATLAB,More1978 ) and the classical homotopy continuation methods (HOMPACK90 \mbox{%DIFAUXCMD \cite{WSMMW1997 }\hspace{0pt}%DIFAUXCMD and the built-in subroutines psolve. m for polynomial systems, GaussNewton.m for non-polynomial systems of the NAClab environment \mbox{%DIFAUXCMD \cite{ZL2013}}\hspace{0pt}%DIFAUXCMD )}  .
After revision:  with comparison to the traditional trust-region method (the built-in subroutine fsolve.m of the MATLAB environment \mbox{%DIFAUXCMD MATLAB,More1978 ) and the classical homotopy continuation methods (HOMPACK90 \mbox{%DIFAUXCMD \cite{WSMMW1997 }\hspace{0pt}%DIFAUXCMD and the built-in subroutines psolve. m for polynomial systems, GaussNewton.m for non-polynomial systems of the NAClab environment \mbox{%DIFAUXCMD \cite{ZL2013}}\hspace{0pt}%DIFAUXCMD )} and NAClab). Furthermore, we analyze the global convergence and the local superlinear convergence of the new method .