Description of fast matrix multiplication algorithm: ⟨8×16×32:2445⟩

Algorithm type

16 X^{4} Y^{8} Z^{4} + X^{2} Y^{8} Z^{3} + 192 X^{4} Y^{4} Z^{4} + 60 X^{2} Y^{8} Z^{2} + 6 X^{2} Y^{7} Z^{3} + 7 X^{2} Y^{7} Z^{2} + 3 X^{2} Y^{6} Z^{3} + 2 X Y^{8} Z^{2} + 115 X^{2} Y^{6} Z^{2} + X^{2} Y^{5} Z^{3} + 7 X Y^{8} Z + 5 X Y^{7} Z^{2} + X^{2} Y^{5} Z^{2} + 2 X^{2} Y^{4} Z^{3} + 8 X Y^{7} Z + X Y^{4} Z^{4} + 38 X^{2} Y^{4} Z^{2} + X Y^{5} Z^{2} + 10 X Y^{4} Z^{3} + 2 X Y^{5} Z + 11 X Y^{4} Z^{2} + X Y^{3} Z^{3} + 793 X^{2} Y^{2} Z^{2} + 105 X Y^{4} Z + 8 X Y^{3} Z^{2} + 2 X^{3} Y Z + 224 X Y^{3} Z + X Y Z^{3} + 8 X^{2} Y Z + 3 X Y Z^{2} + 811 X Y Z

Algorithm definition

The algorithm ⟨8×16×32:2445⟩ is serendipitous tensor product (⟨2×4×8:51⟩ - 17) ⊗ ⟨4×4×4:48⟩ +⟨4×4×12:141⟩ +7⟨4×4×8:96⟩.

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.

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