Description of fast matrix multiplication algorithm: ⟨26 × 32 × 32:14266⟩

Algorithm type

[[1, 1, 1]$2430,[1, 1, 2]$162,[1, 1, 3]$486,[1, 2, 1]$1800,[1, 2, 2]$390,[1, 2, 3]$6,[1, 2, 4]$6,[1, 2, 5]$6,[1, 2, 6]$6,[1, 3, 1]$324,[1, 4, 1]$6,[1, 4, 2]$18,[1, 4, 3]$6,[1, 4, 4]$6,[2, 1, 1]$162,[2, 2, 1]$378,[2, 2, 2]$3939,[2, 2, 3]$6,[2, 2, 4]$45,[2, 2, 5]$30,[2, 2, 6]$147,[2, 4, 1]$6,[2, 4, 2]$672,[2, 4, 3]$12,[2, 4, 4]$131,[2, 4, 6]$1,[2, 4, 8]$1,[2, 4, 10]$1,[2, 4, 12]$1,[2, 6, 1]$12,[2, 6, 2]$114,[2, 8, 2]$1,[2, 8, 4]$3,[2, 8, 6]$1,[2, 8, 8]$1,[3, 1, 1]$486,[3, 2, 2]$12,[3, 4, 1]$6,[3, 4, 2]$12,[3, 4, 3]$96,[3, 4, 4]$102,[4, 2, 2]$51,[4, 4, 1]$6,[4, 4, 2]$129,[4, 4, 3]$102,[4, 4, 4]$1309,[4, 4, 6]$1,[4, 4, 8]$3,[4, 4, 10]$5,[4, 4, 12]$11,[4, 8, 2]$1,[4, 8, 4]$62,[4, 8, 6]$2,[4, 8, 8]$11,[4, 12, 2]$2,[4, 12, 4]$10,[5, 2, 1]$6,[5, 2, 2]$30,[5, 8, 5]$6,[5, 8, 8]$6,[6, 2, 1]$6,[6, 2, 2]$147,[6, 4, 4]$2,[6, 8, 2]$1,[6, 8, 4]$2,[6, 8, 6]$22,[6, 8, 7]$6,[6, 8, 8]$17,[7, 8, 6]$6,[7, 8, 7]$36,[8, 4, 4]$4,[8, 8, 2]$1,[8, 8, 4]$11,[8, 8, 5]$6,[8, 8, 6]$17,[8, 8, 8]$156,[10, 4, 2]$1,[10, 4, 4]$5,[10, 16, 10]$1,[10, 16, 16]$1,[12, 4, 2]$1,[12, 4, 4]$11,[12, 16, 12]$1,[12, 16, 14]$1,[13, 16, 13]$6,[14, 16, 12]$1,[14, 16, 14]$6,[16, 16, 10]$1,[16, 16, 16]$6,[26, 32, 26]$1]

Algorithm definition

The algorithm ⟨26 × 32 × 32:14266⟩ is the (Kronecker) tensor product of ⟨2 × 2 × 2:7⟩ with ⟨13 × 16 × 16:2038⟩.

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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