# Efficiently Correcting Matrix Products

Efficiently Correcting Matrix Products We study the problem of efficiently correcting an erroneous product of two $$n\times n$$ 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 $${\tilde{O}}(n^2+kn)$$ O ~ ( n 2 + k n ) time and a deterministic $${\tilde{O}}(kn^2)$$ O ~ ( k n 2 ) -time algorithm for this problem (where the notation $${\tilde{O}}$$ O ~ suppresses polylogarithmic terms in n and k). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

# Efficiently Correcting Matrix Products

, Volume 79 (2) – Aug 22, 2016
16 pages

/lp/springer_journal/efficiently-correcting-matrix-products-HxfR5CbLIp
Publisher
Springer US
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
D.O.I.
10.1007/s00453-016-0202-3
Publisher site
See Article on Publisher Site

### Abstract

We study the problem of efficiently correcting an erroneous product of two $$n\times n$$ 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 $${\tilde{O}}(n^2+kn)$$ O ~ ( n 2 + k n ) time and a deterministic $${\tilde{O}}(kn^2)$$ O ~ ( k n 2 ) -time algorithm for this problem (where the notation $${\tilde{O}}$$ O ~ suppresses polylogarithmic terms in n and k).

### Journal

AlgorithmicaSpringer Journals

Published: Aug 22, 2016

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