Faculty Publications
Permanent URI for this communityhttps://idr.nitk.ac.in/handle/123456789/18736
Publications by NITK Faculty
Browse
4 results
Search Results
Item Enlarging the convergence ball of the method of parabola for finding zero of derivatives(Elsevier Inc. usjcs@elsevier.com, 2015) Argyros, I.K.; George, S.We present a new technique for enlarging the convergence ball of the method of parabola in order to approximate a zero of derivatives. This approach also leads to more precise error estimates on the distances involved than in earlier studies such as Hua (1974), Ren and Wu (2009) and Wand (1975). These advantages are obtained under the same computational cost on the Lipschitz constants involved as in the earlier studies. Numerical examples are also given to show the advantages over the earlier work. © 2015 Elsevier Inc. All rights reserved.Item Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative(Elsevier Inc. usjcs@elsevier.com, 2015) Argyros, I.K.; George, S.Abstract We present a convergence ball comparison between three iterative methods for approximating a locally unique solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for these methods under hypotheses only on the first Fréchet derivative in contrast to earlier studies such as Adomian (1994) [1], Babajee et al. (2008) [13], Cordero and Torregrosa (2007) [17], Cordero et al. [18], Darvishi and Barati (2007) [19], using hypotheses reaching up to the fourth Fréchet derivative although only the first derivative appears in these methods. This way we expand the applicability of these methods. Numerical examples are also presented in this study. © 2015 Elsevier Inc.Item Unified convergence domains of Newton-like methods for solving operator equations(Elsevier Inc. usjcs@elsevier.com, 2016) Argyros, I.K.; George, S.We present a unified semilocal convergence analysis in order to approximate a locally unique zero of an operator equation in a Banach space setting. Using our new idea of restricted convergence domains we generate smaller Lipschitz constants than in earlier studies leading to the following advantages: weaker sufficient convergence criteria, tighter error estimates on the distances involved and an at least as precise information on the location of the zero. Hence, the applicability of these methods is extended. These advantages are obtained under the same cost on the parameters involved. Numerical examples where the old sufficient convergence criteria cannot apply to solve equations but the new criteria can apply are also provided in this study. © 2016 Elsevier Inc. All rights reserved.Item Local Convergence of Jarratt-Type Methods with Less Computation of Inversion Under Weak Conditions(Taylor and Francis Ltd., 2017) Argyros, I.K.; George, S.We present a local convergence analysis for Jarratt-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Earlier studies cannot be used to solve equations using such methods. The convergence ball and error estimates are given for these methods. Numerical examples are also provided in this study. © 2017, © Vilnius Gediminas Technical University, 2017.