On the Convergence Analysis of a Two-Step Modification of the Gauss-Newton Method

Roman Iakymchuk (1, 2) , Stepan Shakhno (3)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques
2 ISCD - Institut des Sciences du Calcul et des Données
3 Department of Numerical Mathematics

We investigate the convergence of a two-step modification of the Gauss-Newton method applying the generalized Lipschitz condition for the first and second order derivatives. The convergence order as well as the convergence radius of the method are studied and the uniqueness ball of solution of the nonlinear least squares problem is examined. Finally, we carry out numerical experiments on a set of well-known test problems.

Keywords: Lipschitz conditions with L average; radius of convergence; Gauss-Newton type method; Least squares problem

Domains: Optimization and Control [math.OC]; Numerical Analysis [math.NA]

Roman Iakymchuk, Stepan Shakhno. On the Convergence Analysis of a Two-Step Modification of the Gauss-Newton Method. PAMM. Vol. 14. Special issue: 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Mar 2014, Erlangen, Germany. pp.813-814. ⟨hal-00960300v2⟩