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Directional Newton methods
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter, we are concerned with the convergence of the Directional Newton method (DNM), which is used in many areas such us computer graphics and many applied sciences. We obtain weaker convergence criteria, larger ...
Shadowing lemma for operators with chaotic behavior
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
Capítulo del libro "Contemporary study of iterative methods: convergence, dynamics and applications"
Introduction to complex dynamics
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter some dynamical concepts of complex dynamics that will be used in this book are presented. Moreover, some graphics illustrating the theoretical concepts are shown in order to let the reader understand them better.
Newton's method for solving optimal shape design problems
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present some results related to Newton's method in order to extend the solvability of optimal shape design problems. Moreover, some numerical examples are also presented in the chapter.
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 ...
Inexact gauss-newton method for least square problems
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are interested in locating a solution x of the nonlinear least squares problem: minG(x) := 1/2 F(x)TF(x), (8.1) where F is Fréchet-differentiable defined on ℝn with values in ℝm, m ≥ n.
Generalized newton method with applications
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are interested in the approximately solving the generalized equation: Find x ∈ H such that 0 ∈ F(x) + T(x). (16.1) where F : H → H is a Fr→chet differentiable function, H is a Hilbert space and T : H ⇉ ...
Iterative algorithms II
(Nova Science Publishers, 2016-01)
The study of iterative methods began several years ago in order to find the solutions of problems where mathematicians cannot find a solution in closed form. In this way, different studies related to different methods with ...
Gauss-Newton method
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present the local convergence analysis of Gauss–Newton method using the idea of restricted convergence domains, which allows us to improve previous results. Finally, some special cases and a numerical ...
Müller’s method
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are concerned with approximating a solution of the equation f(x) = 0, (15.1) where f is defined on an open domain or closed domain D on a real space ℝ.