Description of fast matrix multiplication algorithm: ⟨8×21×32:3220⟩

Algorithm type

20⁢X8⁢Y8⁢Z8+20⁢X4⁢Y12⁢Z4+48⁢X4⁢Y8⁢Z4+48⁢X2⁢Y12⁢Z2+48⁢X⁢Y12⁢Z+204⁢X4⁢Y4⁢Z4+48⁢X2⁢Y8⁢Z2+48⁢X⁢Y9⁢Z+192⁢X2⁢Y6⁢Z2+192⁢X2⁢Y4⁢Z2+48⁢X⁢Y6⁢Z+720⁢X2⁢Y2⁢Z2+144⁢X⁢Y4⁢Z+432⁢X⁢Y3⁢Z+144⁢X⁢Y2⁢Z+864⁢X⁢Y⁢Z20X8Y8Z820X4Y12Z448X4Y8Z448X2Y12Z248XY12Z204X4Y4Z448X2Y8Z248XY9Z192X2Y6Z2192X2Y4Z248XY6Z720X2Y2Z2144XY4Z432XY3Z144XY2Z864XYZ20*X^8*Y^8*Z^8+20*X^4*Y^12*Z^4+48*X^4*Y^8*Z^4+48*X^2*Y^12*Z^2+48*X*Y^12*Z+204*X^4*Y^4*Z^4+48*X^2*Y^8*Z^2+48*X*Y^9*Z+192*X^2*Y^6*Z^2+192*X^2*Y^4*Z^2+48*X*Y^6*Z+720*X^2*Y^2*Z^2+144*X*Y^4*Z+432*X*Y^3*Z+144*X*Y^2*Z+864*X*Y*Z

Algorithm definition

The algorithm ⟨8×21×32:3220⟩ is the (Kronecker) tensor product of ⟨2×3×4:20⟩ with ⟨4×7×8:161⟩.

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.


Back to main table