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Numerical validation of compensated algorithms with stochastic arithmetic

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  • Graillat, Stef
  • Jézéquel, Fabienne
  • Picot, Romain

Abstract

Compensated algorithms consist in computing the rounding errors of individual operations and then adding them later on to the computed result. This makes it possible to increase the accuracy of the computed result efficiently. Computing the rounding error of an individual operation is possible through the use of a so-called error-free transformation. In this article, we show that it is possible to validate the result of compensated algorithms using stochastic arithmetic. We study compensated algorithms for summation, dot product and polynomial evaluation. We prove that the use of the random rounding mode inherent to stochastic arithmetic does not change much the accuracy of compensated methods. This is due to the fact that error-free transformations are no more exact but still sufficiently accurate to improve the numerical quality of results.

Suggested Citation

  • Graillat, Stef & Jézéquel, Fabienne & Picot, Romain, 2018. "Numerical validation of compensated algorithms with stochastic arithmetic," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 339-363.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:339-363
    DOI: 10.1016/j.amc.2018.02.004
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    References listed on IDEAS

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    1. Du, Peibing & Barrio, Roberto & Jiang, Hao & Cheng, Lizhi, 2017. "Accurate quotient-difference algorithm: Error analysis, improvements and applications," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 245-271.
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    Cited by:

    1. Li, Chuanying & Barrio, Roberto & Xiao, Xiong & Du, Peibing & Jiang, Hao & Quan, Zhe & Li, Kenli, 2023. "PACF: A precision-adjustable computational framework for solving singular values," Applied Mathematics and Computation, Elsevier, vol. 440(C).

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    1. Li, Chuanying & Barrio, Roberto & Xiao, Xiong & Du, Peibing & Jiang, Hao & Quan, Zhe & Li, Kenli, 2023. "PACF: A precision-adjustable computational framework for solving singular values," Applied Mathematics and Computation, Elsevier, vol. 440(C).

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