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Advances in the Semilocal Convergence of Newton’s Method with Real-World Applications

Author

Listed:
  • Ioannis K. Argyros

    (Department of Mathematics Sciences Lawton, Cameron University, Lawton, OK 73505, USA)

  • Á. Alberto Magreñán

    (Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain)

  • Lara Orcos

    (Departamento de Matemática Aplicada, Universidad Politècnica de València, 46022 València, Spain)

  • Íñigo Sarría

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño; Spain)

Abstract

The aim of this paper is to present a new semi-local convergence analysis for Newton’s method in a Banach space setting. The novelty of this paper is that by using more precise Lipschitz constants than in earlier studies and our new idea of restricted convergence domains, we extend the applicability of Newton’s method as follows: The convergence domain is extended; the error estimates are tighter and the information on the location of the solution is at least as precise as before. These advantages are obtained using the same information as before, since new Lipschitz constant are tighter and special cases of the ones used before. Numerical examples and applications are used to test favorable the theoretical results to earlier ones.

Suggested Citation

  • Ioannis K. Argyros & Á. Alberto Magreñán & Lara Orcos & Íñigo Sarría, 2019. "Advances in the Semilocal Convergence of Newton’s Method with Real-World Applications," Mathematics, MDPI, vol. 7(3), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:299-:d:216781
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    Cited by:

    1. Cristina Amorós & Ioannis K. Argyros & Daniel González & Ángel Alberto Magreñán & Samundra Regmi & Íñigo Sarría, 2020. "New Improvement of the Domain of Parameters for Newton’s Method," Mathematics, MDPI, vol. 8(1), pages 1-12, January.

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