Description of fast matrix multiplication algorithm: ⟨8×18×28:2450⟩

Algorithm type

X^{8} Y^{12} Z^{8} + 9 X^{8} Y^{8} Z^{8} + 4 X^{8} Y^{6} Z^{8} + 2 X^{4} Y^{14} Z^{4} + 2 X^{8} Y^{4} Z^{8} + 11 X^{4} Y^{12} Z^{4} + 4 X^{2} Y^{16} Z^{2} + 10 X^{4} Y^{10} Z^{4} + 10 X^{2} Y^{14} Z^{2} + 17 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{6} Z^{4} + 10 X^{2} Y^{10} Z^{2} + 102 X^{4} Y^{4} Z^{4} + 14 X^{2} Y^{8} Z^{2} + 24 X^{4} Y^{3} Z^{4} + 12 X^{2} Y^{7} Z^{2} + 24 X^{4} Y^{2} Z^{4} + 128 X^{2} Y^{6} Z^{2} + 24 X Y^{8} Z + 60 X^{2} Y^{5} Z^{2} + 60 X Y^{7} Z + 166 X^{2} Y^{4} Z^{2} + 108 X^{2} Y^{3} Z^{2} + 60 X Y^{5} Z + 340 X^{2} Y^{2} Z^{2} + 84 X Y^{4} Z + 72 X^{2} Y Z^{2} + 372 X Y^{3} Z + 384 X Y^{2} Z + 312 X Y Z

Algorithm definition

The algorithm ⟨8×18×28:2450⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×9×14:350⟩.

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