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Improved local convergence for Euler–Halley-like methods with a parameter

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Abstract

We present a local convergence analysis for Euler–Halley-like methods with a parameter in order to approximate a locally unique solution of an equation in a Banach space setting. Using more flexible Lipschitz-type hypotheses than in earlier studies such as Huang and Ma (Numer Algorith 52:419–433, 2009), we obtain a larger radius of convergence as well as more precise error estimates on the distances involved. Numerical examples justify our theoretical results.

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Authors and Affiliations

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

    Ioannis K. Argyros

  2. Department of Mathematical and Computational Sciences, NIT, Mangalore, Karnataka, India, 575 025

    Santhosh George

Authors
  1. Ioannis K. Argyros
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  2. Santhosh George
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Correspondence to Santhosh George.

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Argyros, I.K., George, S. Improved local convergence for Euler–Halley-like methods with a parameter. Rend. Circ. Mat. Palermo 65, 87–96 (2016). https://doi.org/10.1007/s12215-015-0220-z

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  • DOI: https://doi.org/10.1007/s12215-015-0220-z

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