Description of fast matrix multiplication algorithm: ⟨2×7×8:88⟩

Algorithm type

2XY7Z+4XY6Z+8X2Y3Z2+2XY5Z+16X2Y2Z2+2XY4Z+10XY3Z+10XY2Z+34XYZ2XY7Z4XY6Z8X2Y3Z22XY5Z16X2Y2Z22XY4Z10XY3Z10XY2Z34XYZ2*X*Y^7*Z+4*X*Y^6*Z+8*X^2*Y^3*Z^2+2*X*Y^5*Z+16*X^2*Y^2*Z^2+2*X*Y^4*Z+10*X*Y^3*Z+10*X*Y^2*Z+34*X*Y*Z

Algorithm definition

The algorithm ⟨2×7×8:88⟩ 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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