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Comparing of the behaviour of iterative methods based on different means
(AIP Conference Proceedings, 2020)
Based on the modification of family of iterative processes of Chebyshev-Halley presented by M. Kansal et al. in [2], whose convergence is cubic, we will present in this talk a comparison between the behaviour of some members ...
Digital Escape Room, Using Genial.Ly and A Breakout to Learn Algebra at Secondary Education Level in Spain
(Education Sciences, 2020-10)
One of the main objectives in mathematics education is to motivate students due to the fact that their interest in this area is often very low. The use of different technologies, as well as gamification in the classroom, ...
Proximal Gauss-Newton method
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we extend the solvability of penalized nonlinear least squares problems using the proximal Gauss–Newton method. Moreover, a numerical example validating the theoretical results is also presented.
The majorization method in the Kantorovich theory
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
The goal in this chapter is to present some improvements related to the convergence of Newton's and modified Newton's method by means of introducing and using the center Lipschitz condition. Using both conditions we obtain ...
Multistep modified Newton-Hermitian and Skew-Hermitian Splitting method
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
Newton–Hermitian and Skew-Hermitian Splitting (MMN-HSS) method.
Two-step Newton methods
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we extend the applicability of two-step Newton's method for solving nonlinear equations.
Newton's method
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
The center Lipschitz condition is used in this chapter, together with the Lipschitz condition, in order to obtain weaker convergence criteria to ensure the convergence pf Newton's method. Numerical examples and applications ...
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.