Fractional Newton–Raphson method accelerated with aitken’s method
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- dc.contributor.author Torres Hernandez, Anthony
- dc.contributor.author Brambila Paz, Fernando
- dc.contributor.author Iturrarán Viveros, Ursula
- dc.contributor.author Caballero Cruz, Reyna
- dc.date.accessioned 2024-04-30T10:06:23Z
- dc.date.available 2024-04-30T10:06:23Z
- dc.date.issued 2021
- dc.description.abstract In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order 𝛼 of the derivative is different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.
- dc.format.mimetype application/pdf
- dc.identifier.citation Torres-Hernandez A, Brambila-Paz F, Iturrarán-Viveros U, Caballero-Cruz R. Fractional Newton–Raphson method accelerated with aitken’s method. Anxioms. 2021;10(2):47. DOI: 10.3390/axioms10020047
- dc.identifier.doi http://dx.doi.org/10.3390/axioms10020047
- dc.identifier.issn 2075-1680
- dc.identifier.uri http://hdl.handle.net/10230/59955
- dc.language.iso eng
- dc.publisher MDPI
- dc.relation.ispartof Anxioms. 2021;10(2):47.
- dc.rights © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/4.0/).
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri https://creativecommons.org/licenses/by/4.0/
- dc.subject.keyword Newton–Raphson method
- dc.subject.keyword fractional calculus
- dc.subject.keyword fractional derivative
- dc.subject.keyword Aitken’s method
- dc.title Fractional Newton–Raphson method accelerated with aitken’s method
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/publishedVersion