Local convergence of an at least sixth-order method in Banach spaces
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Date
2019
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Publisher
Birkhauser Verlag AG
Abstract
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.
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Keywords
Banach space, local convergence, majorizing sequences, Newton-like methods, recurrent functions, recurrent relations, Sixth-order methods, three-step
Citation
Journal of Fixed Point Theory and Applications, 2019, 21, 1, pp. -