73 citations · 398 across the 44 of their papers we have counts for
6 papers · 1 filter
Bounding Zolotarev numbers using Faber rational functions
Daniel Rubin, Alex Townsend, Heather Wilber
By closely following a construction by Ganelius, we construct Faber rational functions that allow us to derive tight and explicit bounds on Zolotarev numbers. We use our results to…
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…
Dense networks that do not synchronize and sparse ones that do
Alex Townsend, Michael Stillman, Steven H. Strogatz
For any network of identical Kuramoto oscillators with identical positive coupling, there is a critical connectivity above which the system is guaranteed to converge to the in-phas…
A sparse spectral method on triangles
Sheehan Olver, Alex Townsend, Geoff Vasil
In this paper, we demonstrate that many of the computational tools for univariate orthogonal polynomials have analogues for a family of bivariate orthogonal polynomials on the tria…
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…
FEAST for differential eigenvalue problems
Andrew Horning, Alex Townsend
An operator analogue of the FEAST matrix eigensolver is developed to compute the discrete part of the spectrum of a differential operator in a region of interest in the complex pla…