Local convergence of the Gauss-Newton-Kurchatov method under generalized Lipschitz conditions

  • S.M. Shakhno Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
  • H.P. Yarmola Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine https://orcid.org/0000-0002-8986-2509
Keywords: Gauss-Newton-Kurchatov method, local convergence, Fréchet derivative, divided difference, generalized Lipschitz condition, convergence domain
Published online: 2021-07-28

Abstract


We investigate the local convergence of the Gauss-Newton-Kurchatov method for solving nonlinear least squares problems. This method is a combination of Gauss-Newton and Kurchatov methods and it is used for problems with the decomposition of the operator. The convergence analysis of the method is performed under the generalized Lipshitz conditions. The conditions of convergence, radius and the convergence order of the considered method are established. Given numerical examples confirm the theoretical results.

Article metrics
PDF downloads: 82
Abstract views: 388
How to Cite
(1)
ShakhnoS.; YarmolaH. Local Convergence of the Gauss-Newton-Kurchatov Method under Generalized Lipschitz Conditions. Carpathian Math. Publ. 2021, 13, 305-314.