2 citations · 2 across the 6 of their papers we have counts for
6 papers
Lightning Helmholtz Solver
Henry Ginn, Lloyd N. Trefethen
In this dissertation we have applied Trefethen and Gopal's Lightning Method to solve the Helmholtz equation in the exterior of two dimensional piecewise smooth domains. The backgro…
AAA rational approximation on a continuum
Toby Driscoll, Yuji Nakatsukasa, Lloyd N. Trefethen
AAA rational approximation has normally been carried out on a discrete set, typically hundreds or thousands of points in a real interval or complex domain. Here we introduce a cont…
Sigmoid functions and multiscale resolution of singularities
Daan Huybrechs, Lloyd N. Trefethen
In this short, conceptual paper we observe that essentially the same mathematics applies in three contexts with disparate literatures: (1) sigmoidal and RBF approximation of smooth…
Spectacularly large expansion coefficients in Müntz's theorem
Lloyd N. Trefethen
Müntz's theorem asserts, for example, that the even powers are dense in . We show that the associated expansions are so inefficient as to have no conc…
AAA interpolation of equispaced data
Daan Huybrechs, Lloyd N. Trefethen
We propose AAA rational approximation as a method for interpolating or approximating smooth functions from equispaced data samples. Although it is always better to approximate from…
Rectangular eigenvalue problems
Behnam Hashemi, Yuji Nakatsukasa, Lloyd N. Trefethen
Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m>>n collocation po…