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ABSTRACT
The CESTAC method (Control and stochastic estimate of rounded calculation) consists in assessing the reliability of the results provided by the computer. Indeed, the computer makes calculations wich use a finite representation (floating point numbers) of real numbers even though these numbers are non-finite. This generates results with uncertainties, rounding errors and invalidation risks. Through the use of a dynamic statistical process, this method allows to determine the number of exact significant decimal digits in the results provided by scientific calculation programmes. This article describes the principles of the method and provides examples concerning the use of the CADNA software (wich allows for this numerical validation).
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Read the articleAUTHORS
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Jean VIGNES: Professor Emeritus, Pierre et Marie Curie University
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René ALT: Professor Emeritus, Pierre et Marie Curie University
INTRODUCTION
The following chapters are devoted to a stochastic approach to the propagation of rounding errors and the influence of data uncertainties on the results delivered by a scientific program.
This is the only method that enables every engineer to answer the question posed above, which in essence is: "What is the exact number of significant decimal places in the results provided by a scientific calculation program?"
The CESTAC method (Control and Stochastic Estimation of Computational Rounding) is detailed in Chapter 2, followed by a presentation of stochastic arithmetic in Chapter 3.
Chapter 4 is devoted to the description and use of CADNA (Control of Accuracy and Debugging of Numerical Algorithms). This software implements the CESTAC method and discrete stochastic arithmetic.
Chapters 5 and 6 are devoted to the contribution of CADNA software to various numerical calculation methods (direct, iterative and approximate), and to examples of its use. Chapter 7 concludes.
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Bibliography
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Norms and standards
- Floating-point arithmetic - IEEE 754 - 01-08
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