Description of fast matrix multiplication algorithm: ⟨21 × 24 × 30:8240⟩

Algorithm type

[[1, 3, 3]$1368,[1, 3, 6]$24,[1, 3, 9]$120,[1, 3, 15]$24,[1, 6, 3]$216,[1, 6, 15]$48,[1, 9, 3]$168,[2, 3, 3]$1656,[2, 3, 6]$64,[2, 3, 9]$80,[2, 3, 15]$16,[2, 6, 3]$312,[2, 6, 6]$1008,[2, 6, 9]$24,[2, 6, 15]$32,[2, 9, 3]$136,[2, 15, 3]$24,[2, 15, 6]$48,[3, 3, 3]$264,[3, 3, 9]$24,[3, 6, 3]$48,[3, 6, 6]$72,[3, 6, 12]$24,[3, 9, 9]$96,[3, 12, 9]$48,[4, 3, 3]$496,[4, 3, 6]$32,[4, 6, 3]$136,[4, 6, 6]$768,[4, 6, 9]$16,[4, 9, 3]$40,[4, 9, 9]$72,[4, 12, 6]$24,[4, 12, 12]$24,[4, 15, 3]$16,[4, 15, 6]$32,[5, 3, 6]$24,[5, 6, 6]$24,[6, 3, 3]$176,[6, 3, 9]$16,[6, 6, 3]$32,[6, 6, 6]$48,[6, 6, 12]$16,[6, 9, 9]$64,[6, 12, 9]$32,[8, 6, 3]$16,[8, 6, 6]$64,[8, 9, 3]$16,[8, 9, 9]$48,[8, 12, 6]$16,[8, 12, 12]$16,[10, 3, 6]$16,[10, 6, 6]$16]

Algorithm definition

The algorithm ⟨21 × 24 × 30:8240⟩ is the (Kronecker) tensor product of ⟨3 × 3 × 6:40⟩ with ⟨7 × 8 × 5:206⟩.

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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