An Inverse Two-Columns Updating Method for solving large-scale nonlinear systems of equations

In this work it is introduced a new quasi-Newton method for solving large-scale nonlinear systems of equations. In this method two columns of the approximation of the inverse Jacobian are updated, in such a way that the two last secant equations are satisfied (when it is possible) at every iteration. The new method is called the Inverse Two-Columns Updating Method (ITCUM). Moreover, it is proposed a right implementation from the point of view of linear algebra and numerical stability. It is presented a local convergence analysis and several numerical tests an a comparison between the performance of this new quasi-Newton method with other quasi-Newton methods, in particular the ICUM (Inverse Column Updating Method) \cite{zam}.