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Floating-point error propagation in iterative methods

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  • Alt, René

Abstract

In this paper, a formal space for the modelization of computer arithmetic and a pseudo-distance defined on this space to study computer iterative sequences is proposed. Some properties if this pseudo-distance are examined and a termination criterion for iterative sequences in this space is given. This termination criterion applies to one-dimensional as well as multi-dimensional sequences.

Suggested Citation

  • Alt, René, 1988. "Floating-point error propagation in iterative methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 505-517.
    • Handle: RePEc:eee:matcom:v:30:y:1988:i:6:p:505-517
    DOI: 10.1016/0378-4754(88)90072-9
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    References listed on IDEAS

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    1. Vignes, J., 1978. "New methods for evaluating the validity of the results of mathematical computations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(4), pages 227-249.
    2. Abadie, J. & Dekhli, F., 1988. "A variant of the CESTAC method and its application to constrained optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 519-529.
    3. Alt, René, 1978. "Error propagation in fourier transforms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(1), pages 37-43.
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    Cited by:

    1. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.

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