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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.
Lavrentiev Regularization methods for Ill-posed equations
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter, we consider the problem of approximately solving the nonlinear ill-posed operator equation of the form F(x) = y, (9.1) where F : D(F) ⊂ X → X is a monotone operator and X is a real Hilbert space. We denote ...
Robust convergence for inexact newton method
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
The main task this chapter is to use the iterative methods to find solutions x of the equation F(x) = 0, (7.1) where D : D ⊂ X → Y is a Fréchet-differentiable operator X, Y are Banach spaces and D ⊂ X. Many problems from ...
Traub's method for multiple roots
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present several convergence results related to the convergence of Traub's method for finding solutions with multiplicity greater than 1. Moreover, we present numerical examples in which the theoretical ...
Developments on the convergence of some iterative methods
(Optimization and Dynamics with Their Applications: Essays in Honor of Ferenc Szidarovszky, 2017)
Iterative methods, play an important role in computational sciences. In this chapter, we present new semilocal and local convergence results for the Newton-Kantorovich method. These new results extend the applicability of ...