Local Convergence of the Gauss-Newton Method for Injective-Overdetermined Systems

Abstract

Abstract. We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10,11,13,14,18]. Special cases and numerical examples are also included in this study.