Description of fast matrix multiplication algorithm: ⟨22×22×22:5566⟩

Algorithm type

2640 X^{3} Y^{3} Z^{3} + 880 X^{3} Y^{3} Z + 220 X^{3} Y^{2} Z^{2} + 220 X^{2} Y^{3} Z^{2} + 220 X^{2} Y^{2} Z^{3} + 22 X^{3} Y^{2} Z + 22 X^{2} Y^{3} Z + 242 X^{2} Y^{2} Z^{2} + 44 X^{2} Y^{2} Z + 902 X Y Z^{3} + 66 X Y Z^{2} + 88 X Y Z

Algorithm definition

The algorithm ⟨22×22×22:5566⟩ 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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