6 citations · 21 across the 14 of their papers we have counts for
16 papers
Fast matrix multiplication via recursive 4x4x4:48 algorithms into practice
Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic +2
We present a fast algorithm for multiplying two 4x4 matrices using 48 multiplications and 204 other operations (addition, subtraction or scaling by a constant) over any ring contai…
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications
Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic
We propose a more accurate variant of an algorithm for multiplying 4x4 matrices using 48 multiplications over any ring containing an inverse of 2. This algorithm achieves an error…
Towards automated generation of fast and accurate algorithms for recursive matrix multiplication
Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic
We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matr…
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications
Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic
The quest for non-commutative matrix multiplication algorithms over non-commutative rings in small dimensions has recently seen significant progress. Specifically, the number of sc…
Strassen's algorithm is not optimally accurate
Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic
We propose a non-commutative algorithm for multiplying 2x2 matrices using 7 coefficient products. This algorithm reaches simultaneously a better accuracy in practice compared to pr…
The tensor rank of 5x5 matrices multiplication is bounded by 98 and its border rank by 89
Alexandre Sedoglavic, Alexey V. Smirnov
We present a non-commutative algorithm for the product of 3x5 by 5x5 matrices using 58 multiplications. This algorithm allows to construct a non-commutative algorithm for multiplyi…