Faculty Publications
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Item Local convergence for multi-point-parametric Chebyshev-Halley-type methods of high convergence order(Elsevier, 2015) Argyros, I.K.; George, S.; Magreñán Ruiz, Á.A.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 earlier methods given by others as special cases. The convergence ball for a class of MMCHTM methods is obtained under weaker hypotheses than before. Numerical examples are also presented in this study. © 2014 Elsevier B.V. All rights reserved.Item Enhancing the applicability of Chebyshev-like method(Academic Press Inc., 2024) George, S.; Bate, I.; M, M.; Godavarma, C.; Senapati, K.Ezquerro and Hernandez (2009) studied a modified Chebyshev's method to solve a nonlinear equation approximately in the Banach space setting where the convergence analysis utilizes Taylor series expansion and hence requires the existence of at least fourth-order Fréchet derivative of the involved operator. No error estimate on the error distance was given in their work. In this paper, we obtained the convergence order and error estimate of the error distance without Taylor series expansion. We have made assumptions only on the involved operator and its first and second Fréchet derivative. So, we extend the applicability of the modified Chebyshev's method. Further, we compare the modified Chebyshev method's efficiency index and dynamics with other similar methods. Numerical examples validate the theoretical results. © 2024 Elsevier Inc.