Journal of the
Korean Mathematical Society JKMS

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 \cite{9,10,11,13,17}. Special cases and numerical examples are also included in this study.

Keywords: the Gauss-Newton method, Hilbert spaces, majorant condition, local convergence, radius of convergence, injective-overdetermined systems

MSC numbers: 65G99, 65K10, 47H17, 49M15, 90C30