11 papers · 1 filter
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…
Symbolic Integration in Weierstrass-like Extensions
Shaoshi Chen, Manuel Kauers, Wenqiao Li +2
This paper studies the integration problem in differential fields that may involve quantities reminiscent of the Weierstrass function, which are defined by a first-order nonl…
Exploring the Meta Flip Graph for Matrix Multiplication
Manuel Kauers, Isaac Wood
Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present here improved rank bounds for about thirty matrix formats.
Symmetric Division of Linear Ordinary Differential Operators
Lixin Du, Manuel Kauers
The symmetric product of two ordinary linear differential operators is an operator whose solution set contains the product of any solution of and any…
Bounds for D-Algebraic Closure Properties
Manuel Kauers, Raphael Pages
We provide bounds on the size of polynomial differential equations obtained by executing closure properties for D-algebraic functions. While it is easy to obtain bounds on the orde…
Consequences of the Moosbauer-Poole Algorithms
Manuel Kauers, Isaac Wood
Moosbauer and Poole have recently shown that the multiplication of two matrices requires no more than 93 multiplications in the (possibly non-commutative) coefficient r…