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On the Convergence of Secant-Like Methods

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Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Abstract

In this chapter, our first idea is to improve the speed of convergence of the Secant method by means of iterative processes free of derivatives of the operator in their algorithms. To achieve this, we consider a uniparametric family of Secant-like methods previously constructed. We analyze the semilocal convergence of this uniparametric family of iterative processes by using a technique that consists of a new system of recurrence relations.

This research has been supported in part by the project MTM2014-52016-C2-1-P of the Spanish Ministry of Economy and Competitiveness.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics Sciences, Cameron University, Lawton, OK, USA

    I. K. Argyros

  2. Dept. of Mathematics and Computation, University of La Rioja, Logroño, Spain

    M. A. Hernández-Verón & M. J. Rubio

Authors
  1. I. K. Argyros
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  2. M. A. Hernández-Verón
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  3. M. J. Rubio
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Corresponding author

Correspondence to M. A. Hernández-Verón .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  2. University of Nis, Faculty of Sciences and Mathematics, Aleksandrovac, Serbia

    Ljubiša D. R. Kočinac

  3. Dept. Mathematics and Statistics, University of Victoria, Victoria, BC, Canada

    Hari M. Srivastava

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Argyros, I.K., Hernández-Verón, M.A., Rubio, M.J. (2019). On the Convergence of Secant-Like Methods. In: Dutta, H., Kočinac, L.D.R., Srivastava, H.M. (eds) Current Trends in Mathematical Analysis and Its Interdisciplinary Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-15242-0_5

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