Extending the Applicability of Stirling’s Method

Cristina Amorós, Ioannis K. Argyros, Á. Alberto Magreñán, Samundra Regmi, Rubén González and Juan Antonio Sicilia
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Cristina Amorós: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
Ioannis K. Argyros: Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
Á. Alberto Magreñán: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain
Samundra Regmi: Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
Rubén González: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
Juan Antonio Sicilia: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain

Mathematics, 2019, vol. 8, issue 1, 1-10

Abstract: 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.

Keywords: Stirling’s method; Newton’s method; convergence; Fréchet derivative; banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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