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Extending the convergence domain of the Secant and Moser method in Banach Space
(Journal of Computational and Applied Mathematics, 2015-12)
We present a new semilocal convergence analysis for the Secant and the Moser method in order to approximate a solution of an equation in a Banach space setting. Using the method of recurrent relations and weaker sufficient ...
Optimizing the applicability of a theorem by F. Potra for Newton-like methods
(Applied Mathematics and Computation, 2014-09)
We present a new sufficient semilocal convergence conditions for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these ...
A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative
(Numerical Algorithms, 2016-01)
We study the local convergence of Chebyshev-Halley-type methods of convergence order at least five to approximate a locally unique solution of a nonlinear equation. Earlier studies such as Behl (2013), Bruns and Bailey ...
Expanding the applicability of the gauss-newton method for convex optimization under restricted convergence domains and majorant conditions
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
n this chapter we are concerned with the convex composite optimizations problem. This work is mainly motivated by the work in [17,23].We present a convergence analysis of Gauss-Newton method (defined by Algorithm (GNA) in ...
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 ...