24 citations · 28 across the 7 of their papers we have counts for
7 papers
Exploiting the Structure in Tensor Decompositions for Matrix Multiplication
Manuel Kauers, Jakob Moosbauer, Isaac Wood
We present a new algorithm for fast matrix multiplication using tensor decompositions which have special features. Thanks to these features we obtain exponents lower than what the…
Some New Non-Commutative Matrix Multiplication Algorithms of Size
Manuel Kauers, Jakob Moosbauer
For various , we propose some new algorithms for multiplying an matrix with an matrix over a possibly noncommutative coefficient ring.
Flip Graphs for Matrix Multiplication
Manuel Kauers, Jakob Moosbauer
We introduce a new method for discovering matrix multiplication schemes based on random walks in a certain graph, which we call the flip graph. Using this method, we were able to r…
The FBHHRBNRSSSHK-Algorithm for Multiplication in is still not the end of the story
Manuel Kauers, Jakob Moosbauer
In response to a recent Nature article which announced an algorithm for multiplying -matrices over with only 96 multiplications, two fewer than the previou…
A Normal Form for Matrix Multiplication Schemes
Manuel Kauers, Jakob Moosbauer
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithm…
Good pivots for small sparse matrices
Manuel Kauers, Jakob Moosbauer
For sparse matrices up to size , we determine optimal choices for pivot selection in Gaussian elimination. It turns out that they are slightly better than the pivots ch…
Chevalley Warning type results on abelian groups
Erhard Aichinger, Jakob Moosbauer
We develop a notion of degree for functions between two abelian groups that allows us to generalize the Chevalley Warning Theorems from fields to noncommutative rings or abelian gr…