33 citations · 164 across the 51 of their papers we have counts for
6 papers · 1 filter
On the convergence of Fourier spectral methods involving non-compact operators
Thomas Trogdon
Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations . The framework posits the existence…
Computing the Tracy-Widom Distribution for Arbitrary
Thomas Trogdon, Yiting Zhang
We compute the Tracy-Widom distribution describing the asymptotic distribution of the largest eigenvalue of a large random matrix by solving a boundary-value problem posed by Bloem…
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginibre matrices
Tyler Chen, Anne Greenbaum, Thomas Trogdon
We study the GMRES algorithm applied to linear systems of equations involving a scaled and shifted matrix whose entries are independent complex Gaussians. When the righ…
Stability of the Lanczos algorithm on matrices with regular spectral distributions
Tyler Chen, Thomas Trogdon
We study the stability of the Lanczos algorithm run on problems whose eigenvector empirical spectral distribution is near to a reference measure with well-behaved orthogonal polyno…
A Riemann--Hilbert approach to computing the inverse spectral map for measures supported on disjoint intervals
Cade Ballew, Thomas Trogdon
We develop a numerical method for computing with orthogonal polynomials that are orthogonal on multiple, disjoint intervals for which analytical formulae are currently unknown. Our…
An artificially-damped Fourier method for dispersive evolution equations
Anne Liu, Thomas Trogdon
Computing solutions to partial differential equations using the fast Fourier transform can lead to unwanted oscillatory behavior. Due to the periodic nature of the discrete Fourier…