Description of fast matrix multiplication algorithm: ⟨16×18×27:4420⟩

Algorithm type

36 X^{8} Y^{8} Z^{8} + 36 X^{4} Y^{4} Z^{12} + 144 X^{4} Y^{8} Z^{4} + 264 X^{4} Y^{4} Z^{4} + 144 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{6} Z^{4} + 144 X^{2} Y^{4} Z^{6} + 24 X^{6} Y^{2} Z^{2} + 24 X^{4} Y^{2} Z^{4} + 64 X^{3} Y^{2} Z^{5} + 168 X^{2} Y^{2} Z^{6} + 96 X^{3} Y Z^{5} + 24 X Y^{6} Z^{2} + 48 X^{4} Y^{2} Z^{2} + 600 X^{2} Y^{4} Z^{2} + 60 X^{2} Y^{2} Z^{4} + 144 X Y^{4} Z^{3} + 48 X^{3} Y^{2} Z + 540 X^{2} Y^{2} Z^{2} + 144 X Y^{4} Z + 24 X Y^{3} Z^{2} + 336 X Y^{2} Z^{3} + 48 X^{3} Y Z + 96 X^{2} Y^{2} Z + 48 X^{2} Y Z^{2} + 120 X Y^{2} Z^{2} + 192 X Y Z^{3} + 96 X^{2} Y Z + 360 X Y^{2} Z + 120 X Y Z^{2} + 216 X Y Z

Algorithm definition

The algorithm ⟨16×18×27:4420⟩ is serendipitous tensor product (⟨8×6×9:296⟩ - 12) ⊗ ⟨2×3×3:15⟩ +4⟨6×3×3:40⟩.

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