Description of fast matrix multiplication algorithm: ⟨2×21×22:704⟩

Algorithm type

X Y^{17} Z + 11 X Y^{16} Z + 13 X Y^{15} Z + 5 X^{2} Y^{12} Z^{2} + 4 X Y^{14} Z + 12 X^{2} Y^{11} Z^{2} + 5 X Y^{13} Z + 11 X^{2} Y^{10} Z^{2} + 3 X Y^{12} Z + 12 X^{2} Y^{9} Z^{2} + 18 X Y^{11} Z + 10 X^{2} Y^{8} Z^{2} + 12 X Y^{10} Z + 12 X^{2} Y^{7} Z^{2} + 16 X Y^{9} Z + 9 X^{2} Y^{6} Z^{2} + 11 X Y^{8} Z + 12 X^{2} Y^{5} Z^{2} + 15 X Y^{7} Z + 8 X^{2} Y^{4} Z^{2} + 13 X Y^{6} Z + 37 X^{2} Y^{3} Z^{2} + 16 X Y^{5} Z + 92 X^{2} Y^{2} Z^{2} + 11 X Y^{4} Z + 15 X Y^{3} Z + 39 X Y^{2} Z + 281 X Y Z

Algorithm definition

The algorithm ⟨2×21×22:704⟩ 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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