Description of fast matrix multiplication algorithm: ⟨2×6×7:67⟩

Algorithm type

3X2Y3Z2+XY5Z+14X2Y2Z2+7XY4Z+6XY3Z+9XY2Z+27XYZ3X2Y3Z2XY5Z14X2Y2Z27XY4Z6XY3Z9XY2Z27XYZ3*X^2*Y^3*Z^2+X*Y^5*Z+14*X^2*Y^2*Z^2+7*X*Y^4*Z+6*X*Y^3*Z+9*X*Y^2*Z+27*X*Y*Z

Algorithm definition

The algorithm ⟨2×6×7:67⟩ 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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