Description of fast matrix multiplication algorithm: ⟨2 × 30 × 32:1456⟩

Algorithm type

[[1, 1, 1]$670,[1, 2, 1]$201,[1, 3, 1]$30,[1, 4, 1]$4,[1, 5, 1]$2,[1, 6, 1]$3,[1, 7, 1]$3,[1, 8, 1]$5,[1, 9, 1]$3,[1, 10, 1]$5,[1, 11, 1]$6,[1, 12, 1]$6,[1, 13, 1]$4,[1, 14, 1]$7,[1, 15, 1]$4,[1, 16, 1]$8,[1, 17, 1]$5,[1, 18, 1]$4,[1, 19, 1]$3,[1, 20, 1]$2,[1, 21, 1]$2,[1, 22, 1]$3,[1, 23, 1]$2,[1, 24, 1]$3,[1, 25, 1]$2,[1, 26, 1]$2,[1, 27, 1]$2,[1, 28, 1]$1,[2, 2, 2]$245,[2, 3, 2]$186,[2, 4, 2]$31,[2, 5, 2]$2]

Algorithm definition

The algorithm ⟨2 × 30 × 32:1456⟩ 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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