Efficiently Correcting Matrix Products

Abstract

We study the problem of efficiently correcting an erroneous product of two n× n matrices over a ring. Among other things, we provide a randomized algorithm for correcting a matrix product with at most k erroneous entries running in O~ (n2+ kn) time and a deterministic O~ (kn2) -time algorithm for this problem (where the notation O~ suppresses polylogarithmic terms in n and k).