Coppersmith–Winograd algorithm: Difference between revisions

Revision as of 14:28, 7 March 2006

Revision as of 21:34, 7 March 2006

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In the [[mathematics|mathematical]] discipline of [[linear algebra]], the '''Coppersmith-Winograd algorithm''' is the fastest currently known [[algorithm]] for square [[matrix multiplication]]. It can multiply two <math>n \times n</math> matrices in <math>O(n^{2.376})</math> time. This is an improvement over the trivial <math>O(n^3)</math> time algorithm and the <math>n^{2.807}</math> time [[Strassen algorithm]]. According to [[Strassman hypotesis]] itIt might be possible to improve the exponent further; however, the exponent must be at least 2 (because an <math>n \times n</math> matrix has <math>n^2</math> values, and all of them have to be read at least once to calculate the exact result). The Coppersmith-Winograd algorithm is frequently used as building block in other algorithms to prove theoretical time bounds, but it appears to be not particularly practical for implementations.

A newer approach by [[Henry Cohn]], [[Robert Kleinberg]], [[Balázs Szegedy]] and [[Christopher Umans]] gets the exponent 2.41 via a [[group-theoretic]] approach.