Description of fast matrix multiplication algorithm: ⟨2×17×18:468⟩

Algorithm type

[[1, 1, 1]$181,[1, 2, 1]$28,[1, 3, 1]$13,[1, 4, 1]$10,[1, 5, 1]$15,[1, 6, 1]$9,[1, 7, 1]$13,[1, 8, 1]$10,[1, 9, 1]$15,[1, 10, 1]$3,[1, 11, 1]$5,[1, 12, 1]$11,[1, 13, 1]$10,[1, 14, 1]$1,[2, 2, 2]$60,[2, 3, 2]$26,[2, 4, 2]$7,[2, 5, 2]$10,[2, 6, 2]$8,[2, 7, 2]$10,[2, 8, 2]$9,[2, 9, 2]$10,[2, 10, 2]$4]

Algorithm definition

The algorithm ⟨2×17×18:468⟩ 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

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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