Description of fast matrix multiplication algorithm: ⟨2×23×24:840⟩

Algorithm type

[[1, 1, 1]$386,[1, 2, 1]$122,[1, 3, 1]$4,[1, 4, 1]$4,[1, 5, 1]$4,[1, 6, 1]$4,[1, 7, 1]$8,[1, 8, 1]$4,[1, 9, 1]$4,[1, 10, 1]$4,[1, 11, 1]$6,[1, 12, 1]$2,[1, 13, 1]$2,[1, 14, 1]$2,[1, 15, 1]$2,[1, 16, 1]$2,[1, 17, 1]$2,[1, 18, 1]$4,[1, 19, 1]$2,[1, 20, 1]$2,[1, 21, 1]$2,[1, 22, 1]$2,[1, 23, 1]$2,[2, 2, 2]$144,[2, 3, 2]$120]

Algorithm definition

The algorithm ⟨2×23×24:840⟩ 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.

Back to main table