The convergence of quasi-Gauss-Newton methods for nonlinear problems

Quasi-Gauss-Newton methods for nonlinear equations are investigated. A Quasi-Gauss-Newton method is proposed. In this method, the Jacobian is modified by a convex combination of Broydenʹs update and a weighted update. The convergence of the method described by Wang and Tewarson in [1] and the proposed method is proved. Computational evidence is given in support of the relative efficiency of the proposed method.