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 ...

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 ...

In this chapter we will study the convex composite optimizations problem.

Capítulo del libro "Iterative Methods and Their Dynamics with Applications"

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 ...

Recently, Argyros and Ren in [6] studied King-Werner-like methods for approximating a locally unique solution x of equation (formula presented).

Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced ...

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 ...

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 ...

We present a new technique to improve the convergence domain for Newton’s method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newton’s method are ...