References

I want to thank Axel Kemper who sent me this beautiful andĀ  complete bibliography.

MatMultReferences20171031

But even more impressive is the following list:

 

 

Formula Multiplications
(1) 3×3 * 3×2 15 Hopcroft
(2) 3×3 * 3×2 14 Kemper
(4) 3×3 * 3×3 20 Smirnov
(5) 2×3 * 3×3 15 Hopcroft
(6) 2×2 * 2×2 7 Strassen
(8) 3×2 * 2×3 14 Smirnov
(9) 2×2 * 2×3 10 Bini
Total 95

95 products correspond to a complexity of O(n2,829), which is above the Strassen complexity of O(n2,80735). To stay below Strassen, a solution for 5x5x5 must not have more than 91 products. Where, the above algorithms have a matrix format:

SolutionsInBiniFormat

s5x5x5_99.Sedoglavic.bini (addition 31/10/2017)

or if you are inclined to a “pseudo-code” version a much longer list is available here

MM_Solutions_Kemper

5x5x5_99_SedoglavicĀ (addition 31/10/2017)

All algorithms are verified.