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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.
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 ...
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.
Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations
(SeMA Journal, 2015-11)
We study the local convergence of a method presented by Cordero et al. of convergence order at least five to approximate a locally unique solution of a nonlinear equation. These studies show the convergence under hypotheses ...
Generalized equations
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present some developments for the local convergence of Newton's method. Some special cases and a numerical example illuminating the theoretical results are also presented.
Local convergence of fourth and fifth order parametric family of iterative methods in Banach spaces
(Journal of Mathematical Chemistry, 2020-01)
This paper deal with the study of local convergence of fourth and fifth order iterative method for solving nonlinear equations in Banach spaces. Only the premise that the first order Frechet derivative fulfills the Lipschitz ...
Local convergence comparison between frozen Kurchatov and Schmidt–Schwetlick–Kurchatov solvers with applications
(Journal of Computational and Applied Mathematics, 2022-04)
In this work we are going to use the Kurchatov–Schmidt–Schwetlick-like solver (KSSLS) and the Kurchatov-like solver (KLS) to locate a zero, denoted by x∗ of operator F. We define F as F:D⊆B1⟶B2 where B1 and B2 stand for ...
Local and Semi-local convergence for Chebyshev two point like methods with applications in different fields
(Journal of Computational and Applied Mathematics, 2023)
The convergence is developed for a large class of Chebyshev-two point-like methods for solving Banach space valued equations. Both the local as well as the semi-local convergence is provided for these methods under general ...