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Newton-secant methods with values in a cone
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
We study the variational inclusion 0 ∈ F(x) + G(x) + E(x), (17.1) where X, Y are Banach space D ⊂ X is an open set F : D → Y is a smooth operator, G : D → Y is continuous operator, [., .;G] is a divided difference of order ...
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 ...
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 ...
Games math. Adaptive video game to evaluate basic mathematic concepts
(2017-08)
Video games are interesting tools which can help teachers to motivate students so as to reinforce the main concepts related to Euclidean geometry, such as the types of angles, lines, and terms related with the circle and ...
Newton’s method for generalized equations using restricted domains
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are concerned with the study of the generalized equation F(x)+Q(x) ϶ 0, where F : D → H is a nonlinear Fréchet differentiable defined on the open subset D of the Hilbert space H, and Q : H ⇉ H is set-valued ...
Nonlinear Ill-posed equations
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we provide an extended the analysis of the Lavrentiev regularization for nonlinear ill-posed problems F(x) = y, where F : D(F) ⊆ X → X is a nonlinear monotone operator considered in [22].
Lavrentiev Regularization methods for Ill-posed equations
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter, we consider the problem of approximately solving the nonlinear ill-posed operator equation of the form F(x) = y, (9.1) where F : D(F) ⊂ X → X is a monotone operator and X is a real Hilbert space. We denote ...