Description of fast matrix multiplication algorithm: ⟨21 × 21 × 30:7400⟩

Algorithm type

[[1, 3, 3]$1560,[1, 3, 6]$120,[1, 3, 9]$120,[1, 6, 3]$96,[1, 6, 6]$24,[1, 9, 3]$120,[1, 15, 3]$24,[1, 15, 6]$48,[2, 3, 3]$1376,[2, 3, 6]$128,[2, 3, 9]$104,[2, 3, 15]$24,[2, 6, 3]$112,[2, 6, 6]$808,[2, 6, 15]$48,[2, 9, 3]$80,[2, 9, 6]$24,[2, 15, 3]$16,[2, 15, 6]$32,[3, 3, 3]$360,[3, 3, 6]$48,[3, 6, 3]$48,[3, 6, 6]$120,[3, 9, 3]$24,[3, 9, 9]$168,[3, 9, 12]$24,[3, 12, 3]$24,[3, 12, 9]$24,[4, 3, 3]$224,[4, 3, 6]$56,[4, 3, 9]$40,[4, 3, 15]$16,[4, 6, 3]$32,[4, 6, 6]$528,[4, 6, 12]$24,[4, 6, 15]$32,[4, 9, 6]$16,[4, 9, 9]$24,[5, 6, 3]$24,[5, 6, 6]$24,[6, 3, 3]$240,[6, 3, 6]$32,[6, 6, 3]$32,[6, 6, 6]$80,[6, 9, 3]$16,[6, 9, 9]$112,[6, 9, 12]$16,[6, 12, 3]$16,[6, 12, 9]$16,[8, 3, 6]$16,[8, 3, 9]$16,[8, 6, 12]$16,[8, 9, 9]$16,[10, 6, 3]$16,[10, 6, 6]$16]

Algorithm definition

The algorithm ⟨21 × 21 × 30:7400⟩ is the (Kronecker) tensor product of ⟨3 × 3 × 6:40⟩ with ⟨7 × 7 × 5:185⟩.

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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