Description of fast matrix multiplication algorithm: ⟨2×5×7:56⟩

Algorithm type

4X2Y3Z2+10X2Y2Z2+5XY4Z+11XY3Z+7XY2Z+19XYZ4X2Y3Z210X2Y2Z25XY4Z11XY3Z7XY2Z19XYZ4*X^2*Y^3*Z^2+10*X^2*Y^2*Z^2+5*X*Y^4*Z+11*X*Y^3*Z+7*X*Y^2*Z+19*X*Y*Z

Algorithm definition

The algorithm ⟨2×5×7:56⟩ 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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