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Ball convergence of a sixth-order Newton-like method based on means under weak conditions
(Journal of Mathematical Chemistry, 2018-08)
We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative ...
Extending the domain of starting points for Newton's method under conditions on the second derivative
(Journal of Computational and Applied Mathematics, 2018-10)
In this paper, we propose a center Lipschitz condition for the second Frechet derivative together with the use of restricted domains in order to improve the domain of starting points for Newton's method. In addition, we ...
A contemporary study of iterative methods: Convergence, dynamics and applications
(Elsevier, 2018)
A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, ...
Domain of parameters
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present several convergence results related to Newton's method in which we enlarge the domain of parameters, which is one of the main problems in iterative procedure studies. Moreover, several numerical ...
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 ...