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Unified local convergence for newton's method and uniqueness of the solution of equations under generalized conditions in a Banach space
(Mathematics, 2019-05)
Under the hypotheses that a function and its Frechet derivative satisfy some generalized Newton-Mysovskii conditions, precise estimates on the radii of the convergence balls of Newton's method, and of the uniqueness ball ...
Study of local convergence and dynamics of a king-like two-step method with applications
(Mathematics, 2020-07-01)
In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because ...
Local convergence comparison between frozen Kurchatov and Schmidt–Schwetlick–Kurchatov solvers with applications
(Journal of Computational and Applied Mathematics, 2022-04)
In this work we are going to use the Kurchatov–Schmidt–Schwetlick-like solver (KSSLS) and the Kurchatov-like solver (KLS) to locate a zero, denoted by x∗ of operator F. We define F as F:D⊆B1⟶B2 where B1 and B2 stand for ...
Local and Semi-local convergence for Chebyshev two point like methods with applications in different fields
(Journal of Computational and Applied Mathematics, 2023)
The convergence is developed for a large class of Chebyshev-two point-like methods for solving Banach space valued equations. Both the local as well as the semi-local convergence is provided for these methods under general ...