Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions

Abstract

The technique of using the restricted convergence region is applied to study a semilocal convergence of the Newton–Kurchatov method. The analysis is provided under weak conditions for the derivatives and the first order divided differences. Consequently, weaker sufficient convergence criteria and more accurate error estimates are retrieved. A special case of weak conditions is also considered.

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

“…. , generated by (5), is well defined, remains in Ω, and converges to x * . Moreover, the following error estimates hold for all k ≥ 0:…”

“…In this paper, we provide the local convergence analysis of the Gauss-Newton-Kurchatov method (5). There are two main approaches to the study the convergence of iterative methods: a local and semilocal convergence analysis.…”