A Refined Probabilistic Error Bound for Sums

04/13/2021

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by   Eric Hallman, et al.

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This paper considers a probabilistic model for floating-point computation in which the roundoff errors are represented by bounded random variables with mean zero. Using this model, a probabilistic bound is derived for the forward error of the computed sum of n real numbers. This work improves upon existing probabilistic bounds by holding to all orders, and as a result provides informative bounds for larger problem sizes.