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The effect of rounding errors on Newton methods

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Abstract

In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newtonlike methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitztype hypotheses on the second Fréchet-derivative instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover, we show that the ratio of convergence improves under our conditions. Furthermore, we provide a wider choice of initial guesses than before. Finally, a numerical example is provided to show that our results compare favorably with earlier ones.

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Authors and Affiliations

  1. Department of Mathematics, Cameron University, 73505, Lawton, IK

    Ioannis K. Argyros

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  1. Ioannis K. Argyros
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Correspondence to Ioannis K. Argyros.

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Argyros, I.K. The effect of rounding errors on Newton methods. Korean J. Comput. & Appl. Math. 7, 533–540 (2000). https://doi.org/10.1007/BF03012266

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  • DOI: https://doi.org/10.1007/BF03012266

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