Derives non-asymptotic probabilistic perturbation and roundoff error bounds for inner products that scale as sqrt(n) rather than n, using Azuma's inequality and martingales, with experiments showing orders-of-magnitude improvement over deterministic bounds.
Comp., 56 (1991), pp
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Probabilistic Error Analysis for Inner Products
Derives non-asymptotic probabilistic perturbation and roundoff error bounds for inner products that scale as sqrt(n) rather than n, using Azuma's inequality and martingales, with experiments showing orders-of-magnitude improvement over deterministic bounds.