Browsing by Author "Khattri, S.K."
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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 An improved semilocal convergence analysis for the Halley's method(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 Local convergence of an at least sixth-order method in Banach spaces(2019) Argyros, I.K.; Khattri, S.K.; George, S.We present a local convergence analysis of an at least sixth-order family of methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. The semilocal convergence analysis of this method was studied by Amat et al. in (Appl Math Comput 206:164 174, 2008; Appl Numer Math 62:833 841, 2012). This work provides computable convergence ball and computable error bounds. Numerical examples are also provided in this study. 2019, Springer Nature Switzerland AG.Item Local convergence of an at least sixth-order method in Banach spaces(Birkhauser Verlag AG, 2019) Argyros, I.K.; Khattri, S.K.; George, S.We present a local convergence analysis of an at least sixth-order family of methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. The semilocal convergence analysis of this method was studied by Amat et al. in (Appl Math Comput 206:164–174, 2008; Appl Numer Math 62:833–841, 2012). This work provides computable convergence ball and computable error bounds. Numerical examples are also provided in this study. © 2019, Springer Nature Switzerland AG.Item On the local convergence of a secant like method in a banach space under weak conditions(2016) Argyros, I.K.; Khattri, S.K.; George, S.We present a local convergence analysis of a Secant-like method in a Banach space setting. The method is used to approximate a solution of a nonlinear equation. The sufficient convergence conditions are weaker than in earlier studies. Numerical examples are also given in this work. 2016 International Publications. All rights reserved.Item On the local convergence of a secant like method in a banach space under weak conditions(International Publications internationalpubls@yahoo.com, 2016) Argyros, I.K.; Khattri, S.K.; George, S.We present a local convergence analysis of a Secant-like method in a Banach space setting. The method is used to approximate a solution of a nonlinear equation. The sufficient convergence conditions are weaker than in earlier studies. Numerical examples are also given in this work. © 2016 International Publications. All rights reserved.