LOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD FOR INJECTIVE-OVERDETERMINED SYSTEMS

. We present, under a weak majorant condition, a local conver-gence analysis for the Gauss-Newton method for injective-overdeterminedsystems of equations in a Hilbert space setting. Our results provide un-der the same information a larger radius of convergence and tighter er-ror estimates on the distances involved than in earlier studies such us[10, 11, 13, 14, 18]. Special cases and numerical examples are also in-cluded in this study. 1. IntroductionLet X and Y be Hilbert spaces. Let D ⊆ X be an open set and F :D −→ Y be a continuously Fr´echet-dierentiable operator. In this study weare concerned with the problem of approximating a locally unique solution x ⋆ of the penalized nonlinear least squares problem(1.1) min x∈D k F(x) k 2 .A solution x ⋆ ∈ D of (1.1) is also called a least squares solution of the equationF(x) = 0.Many problems from computational sciences and other disciplines can bebrought in a form similar to equation (1.1) using Mathematical Modeling [3,9, 17]. For example in data tting, we have X = R