14 citations · 82 across the 35 of their papers we have counts for
23 papers · 1 filter
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 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…
Exact computations with quasiseparable matrices
Clément Pernet, Hippolyte Signargout, Gilles Villard
Quasi-separable matrices are a class of rank-structured matriceswidely used in numerical linear algebra and of growing interestin computer algebra, with applications in e.g. the li…
Computing the Characteristic Polynomial of Generic Toeplitz-like and Hankel-like Matrices
Clément Pernet, Hippolyte Signargout, Pierre Karpman +1
New algorithms are presented for computing annihilating polynomials of Toeplitz, Hankel, and more generally Toeplitz+ Hankel-like matrices over a field. Our approach follows works…
Some fast algorithms multiplying a matrix by its adjoint
Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic
We present a non-commutative algorithm for the multiplication of a 2 x 2 block-matrix by its adjoint, defined by a matrix ring anti-homomorphism. This algorithm uses 5 block produc…