Description of fast matrix multiplication algorithm: ⟨16×22×24:4760⟩

Algorithm type

40 X^{8} Y^{8} Z^{8} + 8 X^{6} Y^{6} Z^{8} + 76 X^{4} Y^{8} Z^{4} + 6 X^{2} Y^{12} Z^{2} + 8 X^{4} Y^{6} Z^{4} + 4 X^{2} Y^{8} Z^{4} + 6 X^{6} Y^{4} Z^{2} + 416 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{4} Z^{6} + 6 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 4 X^{4} Y^{2} Z^{4} + 48 X^{3} Y^{3} Z^{4} + 6 X^{2} Y^{6} Z^{2} + 34 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{2} Z^{6} + 2 X^{4} Y^{2} Z^{2} + 592 X^{2} Y^{4} Z^{2} + 22 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 48 X^{2} Y^{3} Z^{2} + 24 X Y^{4} Z^{2} + 36 X^{3} Y^{2} Z + 1190 X^{2} Y^{2} Z^{2} + 12 X Y^{4} Z + 24 X Y^{2} Z^{3} + 36 X^{3} Y Z + 12 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 36 X Y^{3} Z + 204 X Y^{2} Z^{2} + 24 X Y Z^{3} + 12 X^{2} Y Z + 816 X Y^{2} Z + 132 X Y Z^{2} + 804 X Y Z

Algorithm definition

The algorithm ⟨16×22×24:4760⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×11×12:680⟩.

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