Description of fast matrix multiplication algorithm: ⟨2×4×6:39⟩

Algorithm type

X2Y4Z2+4X2Y3Z2+4X2Y2Z2+4XY4Z+8XY3Z+6XY2Z+12XYZX2Y4Z24X2Y3Z24X2Y2Z24XY4Z8XY3Z6XY2Z12XYZX^2*Y^4*Z^2+4*X^2*Y^3*Z^2+4*X^2*Y^2*Z^2+4*X*Y^4*Z+8*X*Y^3*Z+6*X*Y^2*Z+12*X*Y*Z

Algorithm definition

The algorithm ⟨2×4×6:39⟩ 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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