Geodesic
The effect of rounding errors on a certain class of iterative methods
Applicationes Mathematicae, Tome 27 (2000) no. 3, pp. 369-375.

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In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) 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.
DOI : 10.4064/am-27-3-369-375
Keywords: Fréchet derivative, Lipschitz conditions, Newton-like method, inexact Newton-like method, Banach space

Ioannis Argyros 1

1 
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Ioannis Argyros. The effect of rounding errors on a certain class of iterative methods. Applicationes Mathematicae, Tome 27 (2000) no. 3, pp. 369-375. doi : 10.4064/am-27-3-369-375. http://geodesic.mathdoc.fr/articles/10.4064/am-27-3-369-375/

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