Description of fast matrix multiplication algorithm: ⟨2 × 3 × 4:20⟩

Algorithm type

[[1, 1, 1]$12,[1, 3, 1]$4,[2, 2, 2]$4]

Algorithm definition

The algorithm ⟨2 × 3 × 4:20⟩ is taken from:

John Edward Hopcroft and Leslie R. Kerr. On minimizing the number of multiplication necessary for matrix multiplication. SIAM Journal on Applied Mathematics, 20(1), January 1971. [DOI]

Algorithm description

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

Algorithm symmetries

The following group of 8 isotropies acts as a permutation group on algorithm tensor representation:

maple tensor representation (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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