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King-Werner-type methods of order 1 + √2
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Iterative methods are used to generate a sequence of approximating a solution x of the nonlinear equation F(x) = 0, (10.1) where F is Fréchet-differentiable operator defined on a convex subset D of a Banach space X with ...
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 ...
Comparing of the behaviour of iterative methods based on different means
(AIP Conference Proceedings, 2020)
Based on the modification of family of iterative processes of Chebyshev-Halley presented by M. Kansal et al. in [2], whose convergence is cubic, we will present in this talk a comparison between the behaviour of some members ...
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 ...
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 ...