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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.
Directional Newton methods
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter, we are concerned with the convergence of the Directional Newton method (DNM), which is used in many areas such us computer graphics and many applied sciences. We obtain weaker convergence criteria, larger ...
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 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.
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.
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 ...
Convergence of iterative methods for multiple zeros
(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 order family of iterative methods
Gauss-Newton method for convex composite optimization
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we extend the solvability of convex composite optimization problems using Gauss–Newton method. We present the algorithm and study the regularity. Then we present the semilocal convergence study and finish ...