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Extending the mesh independence for solving nonlinear equations using restricted domains
(International Journal of Applied and Computational Mathematics, 2017-12)
The mesh independence principle states that, if Newton’s method is used to solve an equation on Banach spaces as well as finite dimensional discretizations of that equation, then the behaviour of the discretized process ...
Inexact Newton Methods on Riemannian Manifolds
(Advances in iterative methods for nonlinear equations, 2016)
In this chapter we study of the Inexact Newton Method in order to solve problems on a Riemannian Manifold. We present standard notation and previous results on Riemannian manifolds. A local convergence study is presented ...
Advances in the Semilocal Convergence of Newton's Method with Real-World Applications
(Mathematics, 2019-03-24)
The aim of this paper is to present a new semi-local convergence analysis for Newton's method in a Banach space setting. The novelty of this paper is that by using more precise Lipschitz constants than in earlier studies ...
Study of a high order family: Local convergence and dynamics
(Mathematics, 2019-03-01)
The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a ...
A contemporary study of iterative methods: Convergence, dynamics and applications
(Elsevier, 2018)
A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, ...
Secant-like methods
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we study the problem of finding a locally unique solution x of equation F(x) = 0, (13.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space χ with values in a Banach ...
Gauss-newton method with applications to convex optimization
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we will study the convex composite optimizations problem.
Preface
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Capítulo del libro "Iterative Methods and Their Dynamics with Applications"
Extending the kantorovich theory for solving equations
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Let X, Y be Banach spaces, D ⊂ X be convex, F : D ⊂ X → Y be a Fréchet differentiable operator. We shall determine a solution x of the equation F(x) = 0, Many problems from Applied Sciences can be solved finding the solutions ...
King-werner-like methods free of derivatives
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Recently, Argyros and Ren in [6] studied King-Werner-like methods for approximating a locally unique solution x of equation (formula presented).