Methods with Successive and Parallel Approximations of Inverse Operator for the Nonlinear Least Squares Problem

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

For solving the nonlinear least-square problem, we propose iterative methods that use successive and parallel approximations of the inverse operator instead of solving a linear system of equations. The convergence order as well as the convergence radius of the proposed methods are studied. Finally, we carry out numerical experiments on a set of test problems.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Roman Iakymchuk, Stepan Shakhno. Methods with Successive and Parallel Approximations of Inverse Operator for the Nonlinear Least Squares Problem. PAMM. Vol. 15. Special issue: 86th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Mar 2015, Lecce, Italy. pp.569-570. ⟨hal-01175314⟩