Description of fast matrix multiplication algorithm: ⟨16×18×24:3920⟩

Algorithm type

16 X^{8} Y^{12} Z^{12} + 32 X^{8} Y^{12} Z^{10} + 24 X^{4} Y^{12} Z^{12} + 48 X^{4} Y^{12} Z^{10} + 64 X^{8} Y^{6} Z^{6} + 12 X^{8} Y^{4} Z^{4} + 256 X^{4} Y^{6} Z^{6} + 192 X^{4} Y^{6} Z^{5} + 240 X^{2} Y^{6} Z^{6} + 288 X^{2} Y^{6} Z^{5} + 12 X^{4} Y^{4} Z^{4} + 24 X^{4} Y^{4} Z^{2} + 384 X^{4} Y^{3} Z^{3} + 96 X^{4} Y^{2} Z^{2} + 24 X^{2} Y^{4} Z^{2} + 960 X^{2} Y^{3} Z^{3} + 576 X Y^{3} Z^{3} + 96 X^{2} Y^{2} Z^{2} + 144 X^{2} Y^{2} Z + 144 X^{2} Y Z + 144 X Y^{2} Z + 144 X Y Z

Algorithm definition

The algorithm ⟨16×18×24:3920⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×9×12:560⟩.

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