Description of fast matrix multiplication algorithm: ⟨20×22×22:5384⟩

Algorithm type

1956⁢X3⁢Y3⁢Z3+724⁢X3⁢Y3⁢Z+162⁢X3⁢Y2⁢Z2+828⁢X2⁢Y3⁢Z2+162⁢X2⁢Y2⁢Z3+18⁢X3⁢Y2⁢Z+96⁢X2⁢Y3⁢Z+276⁢X2⁢Y2⁢Z2+60⁢X2⁢Y2⁢Z+76⁢X⁢Y3⁢Z+18⁢X⁢Y2⁢Z2+742⁢X⁢Y⁢Z3+44⁢X⁢Y2⁢Z+138⁢X⁢Y⁢Z2+84⁢X⁢Y⁢Z1956X3Y3Z3724X3Y3Z162X3Y2Z2828X2Y3Z2162X2Y2Z318X3Y2Z96X2Y3Z276X2Y2Z260X2Y2Z76XY3Z18XY2Z2742XYZ344XY2Z138XYZ284XYZ1956*X^3*Y^3*Z^3+724*X^3*Y^3*Z+162*X^3*Y^2*Z^2+828*X^2*Y^3*Z^2+162*X^2*Y^2*Z^3+18*X^3*Y^2*Z+96*X^2*Y^3*Z+276*X^2*Y^2*Z^2+60*X^2*Y^2*Z+76*X*Y^3*Z+18*X*Y^2*Z^2+742*X*Y*Z^3+44*X*Y^2*Z+138*X*Y*Z^2+84*X*Y*Z

Algorithm definition

The algorithm ⟨20×22×22:5384⟩ is taken from:

Charles-Éric Drevet, Md. Nazrul Islam, and Éric Schost. Optimization techniques for small matrix multiplication. Theoretical Computer Science, 412(22):2219--2236, May 2011. [ 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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