Description of fast matrix multiplication algorithm: ⟨2×14×15:323⟩

Algorithm type

X^{2} Y^{8} Z^{2} + 2 X Y^{10} Z + 13 X^{2} Y^{7} Z^{2} + 12 X Y^{9} Z + 12 X^{2} Y^{6} Z^{2} + 12 X Y^{8} Z + 10 X^{2} Y^{5} Z^{2} + 16 X Y^{7} Z + 8 X^{2} Y^{4} Z^{2} + 14 X Y^{6} Z + 16 X^{2} Y^{3} Z^{2} + 11 X Y^{5} Z + 37 X^{2} Y^{2} Z^{2} + 10 X Y^{4} Z + 11 X Y^{3} Z + 25 X Y^{2} Z + 113 X Y Z

Algorithm definition

The algorithm ⟨2×14×15:323⟩ is taken from:

John Edward Hopcroft and Leslie R. Kerr. On minimizing the number of multiplication necessary for matrix multiplication. SIAM Journal on Applied Mathematics, 20(1), January 1971. [DOI]

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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