We transform the system of nonlinear equations into a nonlinear programming problem, which is solved by null space algorithms. We do not use standard least square approach. We divide the equations into two groups. One group contains the equations that are treated as equality constraints. The square of other equations is regarded as objective function. Two groups are updated in every step. In essence, two different methods are used for a system of equations in an algorithm.
Applied Mathematics and Computation, to appear