Description of fast matrix multiplication algorithm: ⟨12×16×27:3016⟩

Algorithm type

28 X^{6} Y^{8} Z^{6} + 8 X^{3} Y^{12} Z^{3} + 8 X^{6} Y^{8} Z^{3} + 8 X^{9} Y^{4} Z^{3} + 4 X^{3} Y^{4} Z^{9} + 16 X^{3} Y^{8} Z^{3} + 8 X Y^{12} Z + 16 X^{6} Y^{4} Z^{3} + 224 X^{4} Y^{4} Z^{4} + 28 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z + 64 X^{6} Y^{2} Z^{2} + 64 X^{4} Y^{4} Z^{2} + 28 X^{3} Y^{4} Z^{3} + 64 X^{2} Y^{6} Z^{2} + 32 X^{2} Y^{2} Z^{6} + 16 X Y^{8} Z + 128 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z + 128 X^{2} Y^{4} Z^{2} + 4 X Y^{4} Z^{3} + 16 X^{2} Y^{4} Z + 672 X^{2} Y^{2} Z^{2} + 28 X Y^{4} Z + 128 X^{3} Y Z + 128 X^{2} Y^{2} Z + 128 X Y^{3} Z + 64 X Y Z^{3} + 256 X^{2} Y Z + 256 X Y^{2} Z + 448 X Y Z

Algorithm definition

The algorithm ⟨12×16×27:3016⟩ is the (Kronecker) tensor product of ⟨3×4×3:29⟩ with ⟨4×4×9:104⟩.

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.

Back to main table