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Assessing Numerical Errors

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Numerical Methods and Optimization

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Abstract

Methods are described that use the computer itself for assessing the effect of its rounding errors on the precision of its numerical results. The assessment of the effect of method errors is also considered. The floating-point representation of real numbers and rounding modes available according to IEEE standard 754, with which most of today’s computers comply, are recalled. The cumulative effect of rounding errors is investigated. The main classes of methods available for quantifying numerical errors are presented. A particularly simple yet potentially very useful approach is described, as well as a more sophisticated probabilistic method for evaluating the number of significant decimal digits in a numerical result.

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Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS-SUPÉLEC-Université Paris-Sud, 91192, Gif-sur-Yvette, France

    Éric Walter

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  1. Éric Walter
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Correspondence to Éric Walter .

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Walter, É. (2014). Assessing Numerical Errors. In: Numerical Methods and Optimization. Springer, Cham. https://doi.org/10.1007/978-3-319-07671-3_14

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  • DOI: https://doi.org/10.1007/978-3-319-07671-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07670-6

  • Online ISBN: 978-3-319-07671-3

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