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Article

Extending the Applicability of Stirling’s Method

1
Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
2
Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
3
Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 35; https://doi.org/10.3390/math8010035
Received: 30 November 2019 / Revised: 26 December 2019 / Accepted: 28 December 2019 / Published: 31 December 2019
(This article belongs to the Special Issue Multipoint Methods for the Solution of Nonlinear Equations)
Stirling’s method is considered as an alternative to Newton’s method when the latter fails to converge to a solution of a nonlinear equation. Both methods converge quadratically under similar convergence criteria and require the same computational effort. However, Stirling’s method has shortcomings too. In particular, contractive conditions are assumed to show convergence. However, these conditions limit its applicability. The novelty of our paper lies in the fact that our convergence criteria do not require contractive conditions. Hence, we extend its applicability of Stirling’s method. Numerical examples illustrate our new findings. View Full-Text
Keywords: Stirling’s method; Newton’s method; convergence; Fréchet derivative; banach space Stirling’s method; Newton’s method; convergence; Fréchet derivative; banach space
MDPI and ACS Style

Amorós, C.; Argyros, I.K.; Magreñán, Á.A.; Regmi, S.; González, R.; Sicilia, J.A. Extending the Applicability of Stirling’s Method. Mathematics 2020, 8, 35. https://doi.org/10.3390/math8010035

AMA Style

Amorós C, Argyros IK, Magreñán ÁA, Regmi S, González R, Sicilia JA. Extending the Applicability of Stirling’s Method. Mathematics. 2020; 8(1):35. https://doi.org/10.3390/math8010035

Chicago/Turabian Style

Amorós, Cristina, Ioannis K. Argyros, Á. A. Magreñán, Samundra Regmi, Rubén González, and Juan A. Sicilia. 2020. "Extending the Applicability of Stirling’s Method" Mathematics 8, no. 1: 35. https://doi.org/10.3390/math8010035

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