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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 ⇉ ...
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.
Gauss-Newton method for convex optimization
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
The goal in this chapter is to present a finer convergence analysis of Gauss–Newton method than in earlier works in order to expand the solvability of convex composite optimizations problems. The convergence of Gauss–Newton ...
Directional newton methods and restricted domains
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Let F : D ⊂ ℝn → ℝ be a differentiable function. In computer graphics, we often need to compute and display the intersection C = A ⋂ B of two surfaces A and B in ℝ3 [5], [6]. If the two surfaces are explicitly given by A ...
Osada method
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter the applicability of the Osada method for solving nonlinear equations is extended. Moreover, some examples are also presented illuminating the theoretical results.