Description of fast matrix multiplication algorithm: ⟨16×20×25:4578⟩

Algorithm type

448 X^{4} Y^{8} Z^{4} + 8 X^{2} Y^{12} Z^{2} + 8 X Y^{12} Z + X^{3} Y^{2} Z^{7} + 552 X^{2} Y^{8} Z^{2} + X^{2} Y^{2} Z^{8} + 4 X^{6} Y^{2} Z^{3} + 4 X^{5} Y^{2} Z^{4} + 2 X^{4} Y^{2} Z^{5} + 3 X^{3} Y^{2} Z^{6} + 6 X^{6} Y^{2} Z^{2} + 4 X^{5} Y^{2} Z^{3} + 144 X^{4} Y^{4} Z^{2} + 9 X^{4} Y^{2} Z^{4} + 2 X^{3} Y^{2} Z^{5} + 2 X^{3} Y Z^{6} + 160 X^{2} Y^{4} Z^{4} + 5 X^{2} Y^{2} Z^{6} + X^{2} Y Z^{7} + 104 X Y^{8} Z + X Y^{2} Z^{7} + 2 X^{6} Y^{2} Z + 8 X^{6} Y Z^{2} + 7 X^{5} Y^{2} Z^{2} + 6 X^{4} Y^{2} Z^{3} + 3 X^{4} Y Z^{4} + 8 X^{3} Y^{2} Z^{4} + 2 X^{2} Y^{2} Z^{5} + 3 X^{2} Y Z^{6} + 4 X Y^{2} Z^{6} + 8 X^{6} Y Z + X^{5} Y^{2} Z + 10 X^{5} Y Z^{2} + 23 X^{4} Y^{2} Z^{2} + 8 X^{4} Y Z^{3} + 13 X^{3} Y^{2} Z^{3} + 5 X^{3} Y Z^{4} + 128 X^{2} Y^{4} Z^{2} + 18 X^{2} Y^{2} Z^{4} + 2 X^{2} Y Z^{5} + 14 X^{5} Y Z + 6 X^{4} Y^{2} Z + 21 X^{4} Y Z^{2} + 2 X^{3} Y^{3} Z + 33 X^{3} Y^{2} Z^{2} + 14 X^{3} Y Z^{3} + 144 X^{2} Y^{4} Z + 3 X^{2} Y^{3} Z^{2} + 13 X^{2} Y^{2} Z^{3} + 5 X^{2} Y Z^{4} + 160 X Y^{4} Z^{2} + 2 X Y^{3} Z^{3} + 11 X Y^{2} Z^{4} + 32 X^{4} Y Z + 8 X^{3} Y^{2} Z + 20 X^{3} Y Z^{2} + 6 X^{2} Y^{3} Z + 932 X^{2} Y^{2} Z^{2} + 14 X^{2} Y Z^{3} + 128 X Y^{4} Z + 2 X Y^{3} Z^{2} + 7 X Y^{2} Z^{3} + 47 X^{3} Y Z + 8 X^{2} Y^{2} Z + 35 X^{2} Y Z^{2} + 21 X Y^{3} Z + 12 X Y^{2} Z^{2} + 8 X Y Z^{3} + 325 X^{2} Y Z + 208 X Y^{2} Z + 329 X Y Z^{2} + 280 X Y Z

Algorithm definition

The algorithm ⟨16×20×25:4578⟩ is serendipitous tensor product (⟨8×5×5:144⟩ - 20) ⊗ ⟨2×4×5:32⟩ +10⟨4×4×5:61⟩.

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