21 citations · 39 across the 6 of their papers we have counts for
6 papers · 1 filter
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…
Over-parametrized neural networks as under-determined linear systems
Austin R. Benson, Anil Damle, Alex Townsend
We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural n…
Computing spectral measures of self-adjoint operators
Matthew J. Colbrook, Andrew Horning, Alex Townsend
Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The algorithm can achieve a…
Computing with functions in the ball
Nicolas Boullé, Alex Townsend
A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are nu…
Error localization of best L1 polynomial approximants
Yuji Nakatsukasa, Alex Townsend
An important observation in compressed sensing is that the minimizer of an underdetermined linear system is equal to the minimizer when there exists a sparse solu…
On the compressibility of tensors
Tianyi Shi, Alex Townsend
Tensors are often compressed by expressing them in low rank tensor formats. In this paper, we develop three methodologies that bound the compressibility of a tensor: (1) Algebraic…