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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 ...
A unified convergence analysis for secant-type methods
(Journal of the Korean Mathematical Society, 2014-11)
We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes he computation ...
Relaxed secant-type methods
(Nonlinear Studies, 2014-06)
We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation ...
Improving the domain of parameters for Newton's method with applications
(Journal of Computational and Applied Mathematics, 2017-07)
We present a new technique to improve the convergence domain for Newton’s method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newton’s method are ...
Local convergence of a relaxed two-step Newton like method with applications
(Journal of Mathematical Chemistry, 2017-08)
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 ...
New improved convergence analysis for Newton-like methods with applications
(Journal of Mathematical Chemistry, 2017-08)
We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases ...
Local convergence for multi-point-parametric Chebyshev–Halley-type methods of high
(Journal of Computational and Applied Mathematics, 2015-07)
We present a local convergence analysis for general multi-point-Chebyshev-Halley-type methods (MMCHTM) of high convergence order in order to approximate a solution of an equation in a Banach space setting. MMCHTM includes ...
Extending the applicability of the local and semilocal convergence of Newton's method
(Applied Mathematics and Computation, 2017-01)
We present a local as well a semilocal convergence analysis for Newton's method in a Banach space setting. Using the same Lipschitz constants as in earlier studies, we extend the applicability of Newton's method as follows: ...
Improved local convergence analysis of the Gauss-Newton method under a majorant condition
(Computational Optimization and Applications, 2015-03)
We present a local convergence analysis of Gauss-Newton method for solving nonlinear least square problems. Using more precise majorant conditions than in earlier studies such as Chen (Comput Optim Appl 40:97-118, 2008), ...