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Expanding the applicability of the Secant method under weaker conditions
(Applied Mathematics and Computation, 2015-09)
We present a new semilocal convergence analysis for Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on ...
Improved semilocal convergence analysis in Banach space with applications to chemistry
(Journal of Mathematical Chemistry, 2017)
We present a new semilocal convergence analysis for Secant methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds ...
Local Convergence of the Gauss-Newton Method for Infective-Overdetermined Systems
(Journal of the Korean Mathematical Society, 2014-09)
We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information ...
A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative
(Numerical Algorithms, 2016-01)
We study the local convergence of Chebyshev-Halley-type methods of convergence order at least five to approximate a locally unique solution of a nonlinear equation. Earlier studies such as Behl (2013), Bruns and Bailey ...
Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations
(SeMA Journal, 2015-11)
We study the local convergence of a method presented by Cordero et al. of convergence order at least five to approximate a locally unique solution of a nonlinear equation. These studies show the convergence under hypotheses ...