Description of fast matrix multiplication algorithm: ⟨12×12×16:1421⟩

Algorithm type

7 X^{8} Y^{8} Z^{8} + X^{12} Y^{4} Z^{4} + 2 X^{4} Y^{12} Z^{4} + 2 X^{4} Y^{8} Z^{8} + 2 X^{4} Y^{4} Z^{12} + 4 X^{4} Y^{8} Z^{4} + 4 X^{4} Y^{4} Z^{8} + 91 X^{4} Y^{4} Z^{4} + 12 X^{6} Y^{2} Z^{2} + 24 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{4} Z^{4} + 24 X^{2} Y^{2} Z^{6} + 48 X^{2} Y^{4} Z^{2} + 48 X^{2} Y^{2} Z^{4} + 336 X^{2} Y^{2} Z^{2} + 36 X^{3} Y Z + 72 X Y^{3} Z + 72 X Y^{2} Z^{2} + 72 X Y Z^{3} + 144 X Y^{2} Z + 144 X Y Z^{2} + 252 X Y Z

Algorithm definition

The algorithm ⟨12×12×16:1421⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×6×8:203⟩.

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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