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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 ...
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).
Sixth-order iterative methods
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
We develop sixth-order iterative methods in order to approximate zeros x of the function f defined on the real line. This method can be used to solve many 64problems from computational sciences and other disciplines ...
King-Werner-type methods of order 1 + √2
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Iterative methods are used to generate a sequence of approximating a solution x of the nonlinear equation F(x) = 0, (10.1) where F is Fréchet-differentiable operator defined on a convex subset D of a Banach space X with ...
Expanding the applicability of the gauss-newton method for convex optimization under restricted convergence domains and majorant conditions
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
n this chapter we are concerned with the convex composite optimizations problem. This work is mainly motivated by the work in [17,23].We present a convergence analysis of Gauss-Newton method (defined by Algorithm (GNA) in ...
Ball convergence for eighth order method
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Consider the problem of approximating a locally unique solution x of the nonlinear equation F(x) = 0, (21.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space X with values in a ...