33 citations · 164 across the 51 of their papers we have counts for
55 papers
A Riemann-Hilbert approach to the computation of transform pairs
Kaitlynn Lilly, Thomas Trogdon
We develop a unified methodology that integrates spectral theory, Riemann-Hilbert problems, and inverse scattering theory for the construction and numerical evaluation of transform…
Banded Hermitian Matrices, Matrix Orthogonal Polynomials, and the Toda Lattice
Charbel Abi Younes, Thomas Trogdon
We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure…
Efficient computation of soliton gas primitive potentials
Cade Ballew, Deniz Bilman, Thomas Trogdon
We consider the problem of computing a class of soliton gas primitive potentials for the Korteweg--de Vries equation that arise from the accumulation of solitons on an infinite int…
A Lanczos-Based Algorithmic Approach for Spike Detection in Large Sample Covariance Matrices
Charbel Abi Younes, Xiucai Ding, Thomas Trogdon
We introduce a new approach for estimating the number of spikes in a general class of spiked covariance models without directly computing the eigenvalues of the sample covariance m…
The Akhiezer iteration and inverse-free solvers for Sylvester matrix equations
Cade Ballew, Thomas Trogdon, Heather Wilber
Two inverse-free iterative methods are developed for solving Sylvester matrix equations when the spectra of the coefficient matrices are on, or near, known disjoint subintervals of…
Numerical inverse scattering transform for the defocusing nonlinear Schrödinger equation with box-type initial conditions on a nonzero background
Aikaterini Gkogkou, Barbara Prinari, Thomas Trogdon
We present a method to solve numerically the Cauchy problem for the defocusing nonlinear Schrödinger (NLS) equation with a box-type initial condition (IC) having a nontrivial backg…