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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 ...
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 ...
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 ...
Newton's method for solving optimal shape design problems
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present some results related to Newton's method in order to extend the solvability of optimal shape design problems. Moreover, some numerical examples are also presented in the chapter.
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.
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.