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Numerical accuracy control in fixed-point arithmetic

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  • Ton-That, Long

Abstract

The purpose of this paper is to look at the problem of propagation of round-off errors in fixed-point arithmetic and at various problems of checking solutions of equations already treated by La Porte and Vignes in the case of floating-point arithmetic. We first consider the probabilistic model for the numerical fixed-point representation on a computer, the evaluation of the mean value and of the standard deviation for the absolute error of the assignment operator A, and of elementary operators of arithmetic. We then compute the statistical estimate of the error in the computation of an inner product, and this leads us to the problem of checking the accuracy of the solution of linear systems and of algebraic equations.

Suggested Citation

  • Ton-That, Long, 1988. "Numerical accuracy control in fixed-point arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 553-561.
    • Handle: RePEc:eee:matcom:v:30:y:1988:i:6:p:553-561
    DOI: 10.1016/0378-4754(88)90076-6
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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.
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    Cited by:

    1. Vignes, J., 1988. "Review on stochastic approach to round-off error analysis and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 481-491.

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