Description of fast matrix multiplication algorithm: ⟨16×20×32:5658⟩

Algorithm type

672 X^{4} Y^{4} Z^{4} + 16 X^{6} Y^{2} Z^{2} + 16 X^{2} Y^{6} Z^{2} + 112 X^{4} Y^{2} Z^{2} + 320 X^{2} Y^{4} Z^{2} + 210 X^{2} Y^{2} Z^{4} + 18 X^{2} Y^{2} Z^{3} + 1874 X^{2} Y^{2} Z^{2} + 13 X Y Z^{4} + 36 X^{3} Y Z + 32 X Y^{3} Z + 28 X Y^{2} Z^{2} + 21 X Y Z^{3} + 240 X^{2} Y Z + 672 X Y^{2} Z + 419 X Y Z^{2} + 959 X Y Z

Algorithm definition

The algorithm ⟨16×20×32:5658⟩ is serendipitous tensor product (⟨4×5×8:118⟩ - 22) ⊗ ⟨4×4×4:48⟩ +2⟨4×4×12:141⟩ +8⟨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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