Description of fast matrix multiplication algorithm: ⟨2×6×8:76⟩

Algorithm type

X2Y5Z2+3X2Y4Z2+3XY6Z+5X2Y3Z2+3XY5Z+11X2Y2Z2+9XY4Z+8XY3Z+7XY2Z+26XYZX2Y5Z23X2Y4Z23XY6Z5X2Y3Z23XY5Z11X2Y2Z29XY4Z8XY3Z7XY2Z26XYZX^2*Y^5*Z^2+3*X^2*Y^4*Z^2+3*X*Y^6*Z+5*X^2*Y^3*Z^2+3*X*Y^5*Z+11*X^2*Y^2*Z^2+9*X*Y^4*Z+8*X*Y^3*Z+7*X*Y^2*Z+26*X*Y*Z

Algorithm definition

The algorithm ⟨2×6×8:76⟩ 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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