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Expanding kantorovich’s theorem for solving generalized equations
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In [18], G. S. Silva considered the problem of approximating the solution of the generalized equation F(x) + Q(x) ϶ 0, (22.1) where F : D → H is a Fréchet differentiable function, H is a Hilbert space with inner product ...
Generalized equations and newton’s and method
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In [18], G. S. Silva considered the problem of approximating the solution of the generalized equation F(x)+Q(x) ϶ 0,(11.1) where F : D → H is a Fréchet differentiable function, H is a Hilbert space with inner product ⟨., ...
Halley’s method
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are concerned with the problem of approximating a locally unique solution x* of the nonlinear equation F(x) = 0, where F is twice Fréchet-differentiable operator defined on a nonempty open and convex ...
Local convergence and basins of attraction of a two-step Newton-like method for equations with solutions of multiplicity greater than one
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Let S = ℝ or S = ℂ, D ⊆ S be convex and let F : D → S be a differentiable function. We shall approximate solutions x of the equation F(x) = 0, (5.1) Many problems from Applied Sciences including engineering can be solved ...
Secant-like methods in chemistry
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we provide different semilocal and local results for the convergence of secant-like methods in order to expand the solvability of nonlinear equations. Different numerical examples and chemical applications ...
Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations
(SeMA Journal, 2015-11)
We study the local convergence of a method presented by Cordero et al. of convergence order at least five to approximate a locally unique solution of a nonlinear equation. These studies show the convergence under hypotheses ...
Generalized equations
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present some developments for the local convergence of Newton's method. Some special cases and a numerical example illuminating the theoretical results are also presented.
Laguerre-like method for multiple zeros
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter the applicability of the Laguerre-like method for finding multiple zeros is extended. Numerical examples are also presented.
Newton’s method for k-Fréchet differentiable operators
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
We determine a solution x of the equation F(x) = 0. where X and Y are Banach spaces, D ⊆ X a convex set and F : D → Y is a Fréchet-differentiable operator. In particular, we expand the applicability of the Newton’s method ...
Robust convergence of Newton's method for cone inclusion problem
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
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 ...