Probabilistic Error Analysis for Inner Products

Understand

Probabilistic models are proposed for bounding the forward error in the numerically computed inner product (dot product, scalar product) between of two real $n$-vectors.

• We derive probabilistic perturbation bounds, as well as probabilistic roundoff error bounds for the sequential accumulation of the inner product.
• These bounds are non-asymptotic, explicit, and make minimal assumptions on perturbations and roundoffs.
• The perturbations are represented as independent, bounded, zero-mean random variables, and the probabilistic perturbation bound is based on Azuma's inequality.