On Extended Convergence Domains for the Newton-kantorovich Method
نویسنده
چکیده
We present results on extended convergence domains and their applications for the Newton-Kantorovich method (NKM), using the same information as in previous papers. Numerical examples are provided to emphasize that our results can be applied to solve nonlinear equations using (NKM), in contrast with earlier results which are not applicable in these cases. MSC 2010. 65J15, 65G99, 47H99, 49M15.
منابع مشابه
Extended And Unified Local Convergence For Newton-Kantorovich Method Under w− Conditions With Applications
The goal of this paper is to present a local convergence analysis of Newton’s method for approximating a locally unique solution of an equation in a Banach space setting. Using the gauge function theory and our new idea of restricted convergence regions we present an extended and unified convergence theory. Key–Words: Newton’s method, Banach space, semilocal convergence, gauge function, converg...
متن کاملExtensions of the Newton-Kantorovich Theorem to Variational Inequality Problems
The Newton-Kantorovich theorem is extended to validate the convergence of the NewtonJosephy method for solving variational inequality problem. All the convergence conditions can be tested in digital computer. Moreover, the validation delivers automatically the existence domain of the solution and the error estimate. The ideas are illustrated by numerical results.
متن کاملKantorovich’s type theorems for systems of equations with constant rank derivatives
The famous Newton–Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton’s method to a solution of an equation. Here we present a “Kantorovich type” convergence analysis for the Gauss–Newton’s method which improves the result in [W.M. Häußler, A Kantorovich-type convergence analysis for the Gauss–Newton-method, Numer. Math. 48 (1986) 119–125...
متن کاملNew and Generalized Convergence Conditions for the Newton-kantorovich Method
We present new semilocal convergence theorems for Newton methods in a Banach space. Using earlier general conditions we find more precise error estimates on the distances involved using the majorant principle. Moreover we provide a better information on the location of the solution. In the special case of Newton’s method under Lipschitz conditions we show that the famous Newton–Kantorovich hypo...
متن کاملOn Semilocal Convergence of Inexact Newton
Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...
متن کامل