Faculty Publications
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Item Improved local convergence for Euler–Halley-like methods with a parameter(Springer-Verlag Italia s.r.l. springer@springer.it, 2016) Argyros, I.K.; George, S.We present a local convergence analysis for Euler–Halley-like methods with a parameter in order to approximate a locally unique solution of an equation in a Banach space setting. Using more flexible Lipschitz-type hypotheses than in earlier studies such as Huang and Ma (Numer Algorith 52:419–433, 2009), we obtain a larger radius of convergence as well as more precise error estimates on the distances involved. Numerical examples justify our theoretical results. © 2015, Springer-Verlag Italia.Item Ball Convergence for two-parameter chebyshev-halley-like methods in banach space using hypotheses only on the first derivative(International Publications internationalpubls@yahoo.com, 2017) Argyros, I.K.; George, S.; Verma, R.U.We present a local convergence analysis of a sixth-order method for approximate a locally unique solution of an equation in the Banach space setting. The convergence of this methods is shown in Narang et al. (2016) under hypotheses up to the fourth Fréchet-derivative and the Lipschitz continuity of the third derivative, although only the first derivative appears in the method. In this study we expand the applicability of this method using only hypotheses on the first derivative of the function. Numerical examples are also presented in this study.Item An improved semilocal convergence analysis for the Halley's method(International Publications internationalpubls@yahoo.com, 2018) Argyros, I.K.; Khattri, S.K.; George, S.We expand the applicability of the Halley's method for approximating a locally unique solution of nonlinear equations in a Banach space setting. Our majorizing sequences are finer than in earlier studies such as [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 19, 20, 21, 23] and furthermore developed convergence criteria can be weaker. Finally numerical work is reported that compares favorably to the existing approaches in the literature [6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 24, 25, 26, 28]. © 2018 International Publications. All rights reserved.Item Convergence analysis for a fast class of multi-step chebyshe-halley-type methods under weak conditions(International Publications internationalpubls@yahoo.com, 2020) Argyros, I.K.; George, S.In this study a convergence analysis for a fast multi-step Chebyshe-Halley-type method for solving nonlinear equations involving Banach space valued operator is presented. We introduce a more precise convergence region containing the iterates leading to tighter Lipschitz constants and functions. This way advantages are obtained in both the local as well as the semi-local convergence case under the same computational cost such as: extended convergence domain, tighter error bounds on the distances involved and a more precise information on the location of the solution. The new technique can be used to extend the applicability of other iterative methods. The numerical examples further validate the theoretical results. © 2020, International Publications. All rights reserved.Item Convergence analysis for a fast class of multi-step chebyshev-halley-type methods under weak conditions(International Publications internationalpubls@yahoo.com, 2020) Argyros, I.K.; George, S.In this study a convergence analysis for a fast multi-step Chebyshe-Halley-type method for solving nonlinear equations involving Banach space valued operator is presented. We introduce a more precise convergence region containing the iterates leading to tighter Lipschitz constants and functions. This way advantages are obtained in both the local as well as the semi-local convergence case under the same computational cost such as: extended convergence domain, tighter error bounds on the distances involved and a more precise in-formation on the location of the solution. The new technique can be used to extend the applicability of other iterative methods. The numerical examples further validate the theoretical results. © 2020, International Publications. All rights reserved.