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Extending the Applicability of Stirling’s Method

Author

Listed:
  • 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)

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.

Suggested Citation

  • Cristina Amorós & Ioannis K. Argyros & Á. Alberto Magreñán & Samundra Regmi & Rubén González & Juan Antonio Sicilia, 2019. "Extending the Applicability of Stirling’s Method," Mathematics, MDPI, vol. 8(1), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:35-:d:303851
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    References listed on IDEAS

    as
    1. Cordero, Alicia & Gutiérrez, José M. & Magreñán, Á. Alberto & Torregrosa, Juan R., 2016. "Stability analysis of a parametric family of iterative methods for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 26-40.
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