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le 21 septembre 2023


El-Medhi El Arar

Jeudi 21 septembre 2023 à 10h30
El-Medhi El Arar, Doctorant, LiParad - Université de Versailles Saint-Quentin-en-Yvelines
Title: Bounds on Non-Linear Errors for Variance Computation with Stochastic Rounding
Abstract: Stochastic Rounding (SR) mode is a probabilistic rounding mode: an inexact computation is rounded to the next smaller or larger floating-point number with probability depending on the distances to those numbers. We investigate non-linear errors using SR in variance computation algorithms. We estimate the forward error of computations under SR through two methods: 1 a bound of the variance and Bienaymé–Chebyshev inequality, 2 martingales and Azuma–Hoeffding inequality. We examine two algorithms, "textbook" and "two-pass", both with non-linear errors. We show that they have probabilistic bounds under SR in $O(\sqrt{n}u)$ instead of $nu$ for the deterministic bounds.

Séminaires 2022-2023


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Mise à jour le 20 septembre 2023