Description of fast matrix multiplication algorithm: ⟨24 × 32 × 32:13034⟩

Algorithm type

[[1, 1, 1]$648,[1, 1, 2]$216,[1, 1, 3]$648,[1, 2, 1]$2376,[1, 2, 2]$432,[1, 3, 1]$432,[2, 1, 1]$216,[2, 2, 1]$432,[2, 2, 2]$2484,[2, 2, 4]$108,[2, 2, 6]$324,[2, 4, 2]$1188,[2, 4, 4]$216,[2, 6, 2]$216,[3, 1, 1]$648,[4, 2, 2]$108,[4, 4, 2]$216,[4, 4, 4]$1134,[4, 4, 8]$18,[4, 4, 12]$54,[4, 8, 4]$198,[4, 8, 8]$36,[4, 12, 4]$36,[6, 2, 2]$324,[8, 4, 4]$18,[8, 8, 4]$36,[8, 8, 8]$183,[8, 8, 16]$1,[8, 8, 24]$3,[8, 16, 8]$11,[8, 16, 16]$2,[8, 24, 8]$2,[12, 4, 4]$54,[16, 8, 8]$1,[16, 16, 8]$2,[16, 16, 16]$10,[24, 8, 8]$3]

Algorithm definition

The algorithm ⟨24 × 32 × 32:13034⟩ is the (Kronecker) tensor product of ⟨2 × 2 × 2:7⟩ with ⟨12 × 16 × 16:1862⟩.

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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