Lesson plan
Freivalds' algorithm
Freivalds' algorithm (named after Rūsiņš Mārtiņš Freivalds) is a probabilistic randomized algorithm used to verify matrix multiplication. Given three n × n matrices A , B , and C , a general problem is to verify whether A \times B = C . A naïve algorithm would compute the product A \times B explicitly and compare term by term whether this product equals C . However, the best known matrix multiplication algorithm runs in O(n^{2.372}) time. Freivalds' algorithm utilizes randomization in order to reduce this time bound to O(n^2) with high probability. In O(kn^2) time the algorithm can verify a matrix product with probability of failure less than 2^{-k} .
Article summary
Freivalds' algorithm (named after Rūsiņš Mārtiņš Freivalds) is a probabilistic randomized algorithm used to verify matrix multiplication. Given three n × n matrices A , B , and C , a general problem is to verify whether A \times B = C . A naïve algorithm would compute the product A \times B explicitly and compare term by term whether this product equals C . However, the best known matrix multiplication algorithm runs in O(n^{2.372}) time. Freivalds' algorithm utilizes randomization in order to reduce this time bound to O(n^2) with high probability. In O(kn^2) time the algorithm can verify a matrix product with probability of failure less than 2^{-k} .
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.