Description of fast matrix multiplication algorithm: ⟨20×21×22:5361⟩

Algorithm type

[[1, 1, 1]$105,[1, 1, 2]$143,[1, 1, 3]$724,[1, 2, 1]$79,[1, 2, 2]$9,[1, 3, 1]$37,[2, 1, 1]$10,[2, 1, 2]$1,[2, 1, 3]$9,[2, 2, 1]$61,[2, 2, 2]$473,[2, 2, 3]$153,[2, 3, 1]$76,[2, 3, 2]$630,[3, 2, 1]$46,[3, 2, 2]$162,[3, 2, 3]$153,[3, 3, 1]$687,[3, 3, 3]$1803]

Algorithm definition

The algorithm ⟨20×21×22:5361⟩ is taken from:

Optimization techniques for small matrix multiplication. Theoretical Computer Science, 412(22):2219--2236, May 2011. [ DOI ]

Algorithm description

maple tensor representation (compressed by bzip2);
maple evaluation scheme (compressed by bzip2).

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.

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