Description of fast matrix multiplication algorithm: ⟨16×32×32:8610⟩

Algorithm type

28 X^{8} Y^{16} Z^{8} + 48 X^{8} Y^{12} Z^{8} + 2 X^{12} Y^{8} Z^{4} + 26 X^{8} Y^{8} Z^{8} + 66 X^{4} Y^{16} Z^{4} + 34 X^{4} Y^{14} Z^{4} + 8 X^{8} Y^{8} Z^{4} + 36 X^{4} Y^{12} Z^{4} + 28 X^{4} Y^{10} Z^{4} + 4 X^{6} Y^{8} Z^{2} + 314 X^{4} Y^{8} Z^{4} + 16 X^{4} Y^{8} Z^{2} + 288 X^{4} Y^{6} Z^{4} + 12 X^{6} Y^{4} Z^{2} + 348 X^{4} Y^{4} Z^{4} + 620 X^{2} Y^{8} Z^{2} + 204 X^{2} Y^{7} Z^{2} + 48 X^{4} Y^{4} Z^{2} + 308 X^{2} Y^{6} Z^{2} + 168 X^{2} Y^{5} Z^{2} + 24 X^{3} Y^{4} Z + 876 X^{2} Y^{4} Z^{2} + 96 X^{2} Y^{4} Z + 1432 X^{2} Y^{2} Z^{2} + 1344 X Y^{4} Z + 552 X Y^{3} Z + 1680 X Y Z

Algorithm definition

The algorithm ⟨16×32×32:8610⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×16×16:1230⟩.

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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