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An error bound for fixed-point iterations

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Abstract

We derive an error bound for fixed-point iterationsx n+1=f(x n ) by using monotonicity in the sense of [2]. The new bound is preferable to the classical one which bounds the error in terms of the Lipschitz constant off.

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References

  1. J. M. Ortega and W. C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.

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  2. G. Söderlind,On nonlinear difference and differential equations, BIT 24, 1984.

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Authors and Affiliations

  1. Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44, Stockholm 70, Sweden

    Gustaf Söderlind

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  1. Gustaf Söderlind
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Söderlind, G. An error bound for fixed-point iterations. BIT 24, 391–393 (1984). https://doi.org/10.1007/BF02136040

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  • DOI: https://doi.org/10.1007/BF02136040

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