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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 ...
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 ⟨., ...
The innovation cycle for sustainable ICT education
(IFIP Advances in Information and Communication Technology, 2019)
Usually, the cycle of innovation is sold as a great progress in Education. However, in Education, the cycle of innovation does not exist as we might expect. Innovation is cyclical by itself. Each step of the structure can ...
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 ...
Introduction, Construction, Usage, and Management of MOOCs in China
(Lecture Notes in Educational Technology, 2018)
Chinese higher education which is in the critical stage of comprehensive reform shows great enthusiasm in face of the emerging MOOCs and has begun to consciously pay attention to the development of online education. China’s ...
Overview of Research on Chinese MOOCs
(Lecture Notes in Educational Technology, 2018)
MOOCs have been in the spotlight since its debut in China in 2012. Later, MOOC platforms and relevant courses developed by different organizations sprung up like mushrooms. Now MOOCs can be seen in multiple forms in practice ...
Toward a general theory of point to point iterative processes free of derivatives with quadratic convergence
(AIP Conference Proceedings, 2018)
In this work, we are concerned with the problem of developing a general theory about derivative-free iterative procedures with quadratic convergence. Newton's method is the most used, well-known and studied in order to ...
On a Newton-type family of high-order iterative methods for some matrix functions
(AIP Conference Proceedings, 2018)
The main goal of this paper is to approximate some matrix functions by using a family of high-order Newton-type iterative methods. We analyse the semilocal convergence and the speed of convergence of these methods. Concerning ...
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 ...