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Expanding the convergence domain for Chun-Stanica-Neta family of third order methods in banach spaces
(Journal of the Korean Mathematical Society, 2015-01)
We present a semilocal convergence analysis of a third order method for approximating a locally unique solution of an equation in a Banach space setting. Recently, this method was studied by Chun, Stanica. and Neta. These ...
Expanding the aplicability of secant method with applications
(Bulletin of the Korean Mathematical Society, 2015-05)
We present new sufficient convergence criteria for the convergence of the secant-method to a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center Lipschitz instead of just ...
New semilocal and local convergence analysis for the Secant method
(Applied Mathematics and Computation, 2015-06)
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 ...
Enlarging the convergence domain of secant-like methods for equations
(Taiwanese Journal of Mathematics, 2015-04)
We present two new semilocal convergence analyses for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. These methods include the secant, Newton's ...
On the convergence of an optimal fourth-order family of methods and its dynamics
(Applied Mathematics and Computation, 2015-02)
In this paper, we present the study of the semilocal and local convergence of an optimal fourth-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials ...
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 ...