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Local Convergence Results for an Optimal Iterative Method for Multiple Roots

  • Ramandeep Behl
  • Eulalia MartínezEmail author
  • Fabricio Cevallos
  • Ali Saleh Alshomrani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

In this paper our aim is to perform a local convergence study of a fourth order iterative method in the case of multiple roots. As far as we know, these kind of studies have only been performed for iterative methods of second and third order of convergence in the case of multiple roots. So it is our purpose to analyze the radius of local convergence for higher-order methods. Usually the local convergence radius decreases when the order of the method increases, so it is necessary to study its behavior when we propose a new iterative method. In this sense, we introduce in this paper a new idea for establishing local convergence results of iterative methods for locating multiple zeros, under the assumption of a bounding condition for the \((m + 1)-th\) derivative of the function f(x) in its existence domain. We apply this technique to the modification of the Maheshwari fourth order method for the case of multiple roots. Finally, we perform some numerical examples that confirm the theoretical results established in this paper.

Notes

Acknowledgements

Supported by the project of Generalitat Valenciana Prometeo/2016/089 and MTM2014-52016-C2-2-P of the Spanish Ministry of Science and Innovation.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ramandeep Behl
    • 1
  • Eulalia Martínez
    • 2
    Email author
  • Fabricio Cevallos
    • 3
  • Ali Saleh Alshomrani
    • 1
  1. 1.Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Instituto Universitario de Matemática MultidisciplinarUniversitat Politècnica de ValènciaValenciaSpain
  3. 3.Facultad de Ciencias EconómicasUniversidad laica “Eloy Alfaro” de ManabíMantaEcuador

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