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

Algorithm type

4 X^{2} Y^{2} Z^{2} + 4 X Y^{3} Z + 12 X Y Z

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 LRP 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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