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Domain of parameters
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 ...
On the convergence of inexact two-point Newton-like methods on Banach spaces
We present a unified convergence analysis of Inexact Newton like methods in order to approximate a locally unique solution of a nonlinear operator equation containing a nondifferentiable term in a Banach space setting. The ...
Newton's method for solving optimal shape design problems
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.
Multistep modified Newton-Hermitian and Skew-Hermitian Splitting method
Newton–Hermitian and Skew-Hermitian Splitting (MMN-HSS) method.
Optimizing the applicability of a theorem by F. Potra for Newton-like methods
We present a new sufficient semilocal convergence conditions for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these ...
On the convergence of a Damped Secant method with modified right-hand side vector
We present a convergence analysis for a Damped Secant method with modified right-hand side vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case ...
Starting points for Newton’s method under a center Lipschitz condition for the second derivative
We analyze the semilocal convergence of Newton's method under a center Lipschitz condition for the second derivative of the operator involved different from that used by other authors until now. In particular, we propose ...
Local convergence of a relaxed two-step Newton like method with applications
We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fr,chet derivative ...
On the convergence of a damped Newton-like method with modified right hand side vector
We present a convergence analysis for a damped Newton like method with modified right-hand side vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special ...
New semilocal and local convergence analysis for the Secant method
We present a new convergence analysis, for the Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz ...