DefinePK

Abstract

We have compared the efficiency of two diagonal updating Newton methods for solving systems of nonlinear equations with singular Jacobian. Due to the fact that, the quadratic rate of convergence of Newton method for solving nonlinear systems of equations depends on when the Jacobian is nonsingular in the neighborhood of the solution. Contrary to this condition, i.e. the Jacobian to be singular the convergence is very slow and may even vanished. The two approaches are simple and straight forward to implement. We report on numerous numerical experiments which show that, the proposed algorithms are very efficient and reliable.