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Weaker convergence conditions for the secant method

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Abstract

We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Laboratoire de Mathématiques et Applications, Poitiers University, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Saïd Hilout

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  1. Ioannis K. Argyros
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  2. Saïd Hilout
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Correspondence to Ioannis K. Argyros.

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Argyros, I.K., Hilout, S. Weaker convergence conditions for the secant method. Appl Math 59, 265–284 (2014). https://doi.org/10.1007/s10492-014-0054-6

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  • DOI: https://doi.org/10.1007/s10492-014-0054-6

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