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Extending the domain of starting points for Newton's method under conditions on the second derivative
In this paper, we propose a center Lipschitz condition for the second Frechet derivative together with the use of restricted domains in order to improve the domain of starting points for Newton's method. In addition, we ...
Cohomological Aspects in Semilocal Poisson Geometry
(VELASCO BARRERAS, EDUARDO, 4351)
CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION
(Universidad Católica del Norte, Departamento de Matemáticas, 2006)
Extended convergence results for the Newton–Kantorovich iteration
We present new semilocal and local convergence results for the Newton–Kantorovich method. These new results extend the applicability of the Newton–Kantorovich method on approximate zeros by improving the convergence domain ...
Robust convergence of Newton's method for cone inclusion problem
In this chapter, motivated by the idea of the restricted convergence domains, we present a convergence analysis of Newton's method for cone inclusion problems. The semilocal convergence analysis of Newton's method is also ...
Complexity of an Homotopy Method at the Neighbourhood of a Zero
This paper deals with the enlargement of the region of convergence of Newton's method for solving nonlinear equations defined in Banach spaces. We have used an homotopy method to obtain approximate zeros of the considered ...
A new technique for studying the convergence of Newton’s solver with real life applications
The convergence domain for both the local and semilocal case of Newton’s method for Banach space valued operators is small in general. There is a plethora of articles that have extended the convergence criterion due to ...
Developments on the convergence of some iterative methods
Iterative methods, play an important role in computational sciences. In this chapter, we present new semilocal and local convergence results for the Newton-Kantorovich method. These new results extend the applicability of ...
Weaker conditions for inexact mutitpoint Newton-like methods
In this paper we study the problem of analyzing the convergence both local and semilocal of inexact Newton-like methods for approximating the solution of an equation in which there exists nondifferentiability. We will ...
Gauss-Newton method for convex composite optimization
In this chapter we extend the solvability of convex composite optimization problems using Gauss–Newton method. We present the algorithm and study the regularity. Then we present the semilocal convergence study and finish ...