The Enhanced Fixed Point Method: An Extremely Simple Procedure to Accelerate the Convergence of the Fixed Point Method to Solve Nonlinear Algebraic Equations

Uriel Filobello-Nino, Hector Vazquez-Leal (), Jesús Huerta-Chua, Jaime Martínez-Castillo, Agustín L. Herrera-May, Mario Alberto Sandoval-Hernandez and Victor Manuel Jimenez-Fernandez
Additional contact information
Uriel Filobello-Nino: Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, Xalapa 91000, Veracruz, Mexico
Hector Vazquez-Leal: Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, Xalapa 91000, Veracruz, Mexico
Jesús Huerta-Chua: Instituto Tecnológico Superior de Poza Rica, Tecnológico Nacional de México, Luis Donaldo Colosio Murrieta S/N, Arroyo del Maíz, Poza Rica 93230, Veracruz, Mexico
Jaime Martínez-Castillo: Centro de Investigación en Micro y Nanotecnología, Universidad Veracruzana, Boca del Río 94294, Veracruz, Mexico
Agustín L. Herrera-May: Centro de Investigación en Micro y Nanotecnología, Universidad Veracruzana, Boca del Río 94294, Veracruz, Mexico
Mario Alberto Sandoval-Hernandez: Instituto Tecnológico Superior de Poza Rica, Tecnológico Nacional de México, Luis Donaldo Colosio Murrieta S/N, Arroyo del Maíz, Poza Rica 93230, Veracruz, Mexico
Victor Manuel Jimenez-Fernandez: Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, Xalapa 91000, Veracruz, Mexico

Mathematics, 2022, vol. 10, issue 20, 1-19

Abstract: This work proposes the Enhanced Fixed Point Method (EFPM) as a straightforward modification to the problem of finding an exact or approximate solution for a linear or nonlinear algebraic equation. The proposal consists of providing a versatile method that is easy to employ and systematic. Therefore, it is expected that this work contributes to breaking the paradigm that an effective modification for a known method has to be necessarily long and complicated. As a matter of fact, the method expresses an algebraic equation in terms of the same equation but multiplied for an adequate factor, which most of the times is just a simple numeric factor. The main idea is modifying the original equation, slightly changing it for others in such a way that both have the same solution. Next, the modified equation is expressed as a fixed point problem and the proposed parameters are employed to accelerate the convergence of the fixed point problem for the original equation. Since the Newton method results from a possible fixed point problem of an algebraic equation, we will see that it is relatively easy to get modified versions of the Newton method with orders of convergence major than two. We will see in this work the convenience of this procedure.

Keywords: nonlinear algebraic equations; exact solutions; approximate solutions; fixed point; fixed point theorem; fixed point iteration; Newton method; enhanced fixed point method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/20/3797/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/20/3797/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:20:p:3797-:d:942787

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().