Description of fast matrix multiplication algorithm: ⟨18×20×20:4160⟩

Algorithm type

40 X^{6} Y^{6} Z^{8} + 16 X^{3} Y^{9} Z^{4} + 40 X^{3} Y^{6} Z^{4} + 320 X^{4} Y^{4} Z^{4} + 40 X^{2} Y^{2} Z^{8} + 64 X^{3} Y^{3} Z^{4} + 128 X^{2} Y^{6} Z^{2} + 320 X^{2} Y^{4} Z^{2} + 16 X Y^{3} Z^{4} + 40 X Y^{2} Z^{4} + 1152 X^{2} Y^{2} Z^{2} + 64 X Y Z^{4} + 256 X Y^{3} Z + 640 X Y^{2} Z + 1024 X Y Z

Algorithm definition

The algorithm ⟨18×20×20:4160⟩ is the (Kronecker) tensor product of ⟨2×5×5:40⟩ with ⟨9×4×4:104⟩.

Algorithm description

maple tensor representation (compressed by bzip2);
maple LRP representation (compressed by bzip2);
maple evaluation scheme (compressed by bzip2).

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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