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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.
Laguerre-like method for multiple zeros
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter the applicability of the Laguerre-like method for finding multiple zeros is extended. Numerical examples are also presented.
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 ...
Robust convergence of Newton's method for cone inclusion problem
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter, motivated by the idea of the restricted convergence domains, we present a convergence analysis of Newton's method for cone inclusion problems. The semilocal convergence analysis of Newton's method is also ...
Newton's method to solve equations with solutions of multiplicity greater than one
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter the solvability of equations with multiple roots is expanded using the modified Newton's method. Examples are also presented illuminating the theoretical results.
Convergence planes of iterative methods
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we study the convergence planes associated to a certain class of iterative methods.
Convergence and the dynamics of Chebyshev-Halley type methods
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present a weak convergence analysis and the dynamics of Chebyshev–Halley type methods.
Newton’s method for generalized equations using restricted domains
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are concerned with the study of the generalized equation F(x)+Q(x) ϶ 0, where F : D → H is a nonlinear Fréchet differentiable defined on the open subset D of the Hilbert space H, and Q : H ⇉ H is set-valued ...
Nonlinear Ill-posed equations
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we provide an extended the analysis of the Lavrentiev regularization for nonlinear ill-posed problems F(x) = y, where F : D(F) ⊆ X → X is a nonlinear monotone operator considered in [22].
Convergence and dynamics of a higher order family of iterative methods
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we study the convergence as well as the dynamics of some high convergence order family of iterative methods.