Description of fast matrix multiplication algorithm: ⟨20×20×20:4340⟩

Algorithm type

1920 X^{3} Y^{3} Z^{3} + 720 X^{3} Y^{3} Z + 180 X^{3} Y^{2} Z^{2} + 180 X^{2} Y^{3} Z^{2} + 180 X^{2} Y^{2} Z^{3} + 20 X^{3} Y^{2} Z + 20 X^{2} Y^{3} Z + 200 X^{2} Y^{2} Z^{2} + 40 X^{2} Y^{2} Z + 740 X Y Z^{3} + 60 X Y Z^{2} + 80 X Y Z

Algorithm definition

The algorithm ⟨20×20×20:4340⟩ 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

maple tensor representation (compressed by bzip2);
maple LRP representation (compressed by bzip2);
maple evaluation scheme (compressed by bzip2).

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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