73 citations · 398 across the 44 of their papers we have counts for
6 papers · 2 filters
Parallel algorithms for computing the tensor-train decomposition
Tianyi Shi, Maximilian Ruth, Alex Townsend
The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we…
Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
Matthew J. Colbrook, Alex Townsend
Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. How…
A generalization of the randomized singular value decomposition
Nicolas Boullé, Alex Townsend
The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank approximation of a matrix using matrix-vector products…
Data-driven Algorithms for signal processing with trigonometric rational functions
Heather Wilber, Anil Damle, Alex Townsend
Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requ…
An optimal complexity spectral method for Navier--Stokes simulations in the ball
Nicolas Boullé, Jonasz Słomka, Alex Townsend
We develop a spectral method for solving the incompressible generalized Navier--Stokes equations in the ball with no-flux and prescribed slip boundary conditions. The algorithm ach…
Learning elliptic partial differential equations with randomized linear algebra
Nicolas Boullé, Alex Townsend
Given input-output pairs of an elliptic partial differential equation (PDE) in three dimensions, we derive the first theoretically-rigorous scheme for learning the associated Green…