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ArticleOriginal scientific text

Title

The effect of rounding errors on a certain class of iterative methods

Authors 1

Affiliations

  1. Cameron University, Department of Mathematics, Lawton, OK 73505, U.S.A.

Abstract

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.

Keywords

ENG
Fréchet derivative, Lipschitz conditions, Newton-like method, inexact Newton-like method, Banach space

Bibliography

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Applicationes Mathematicae
2000/27/3
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Pages:
369-375
Main language of publication
English
Received
1999-12-22
Published
2000
Exact and natural sciences