14 citations · 82 across the 35 of their papers we have counts for
37 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…
Computing Krylov iterates in the time of matrix multiplication
Vincent Neiger, Clément Pernet, Gilles Villard
Krylov methods rely on iterated matrix-vector products for an matrix and vectors . The space spanned by all iterates admits a pa…
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…