33 citations · 164 across the 51 of their papers we have counts for
5 papers · 1 filter
A Riemann--Hilbert approach to the perturbation theory for orthogonal polynomials: Applications to numerical linear algebra and random matrix theory
Xiucai Ding, Thomas Trogdon
We establish a new perturbation theory for orthogonal polynomials using a Riemann--Hilbert approach and consider applications in numerical linear algebra and random matrix theory.…
The conjugate gradient algorithm on a general class of spiked covariance matrices
Xiucai Ding, Thomas Trogdon
We consider the conjugate gradient algorithm applied to a general class of spiked sample covariance matrices. The main result of the paper is that the norms of the error and residu…
The Numerical Unified Transform Method for the Nonlinear Schrödinger equation on the half-line
Xin Yang, Bernard Deconinck, Thomas Trogdon
We implement the Numerical Unified Transform Method to solve the Nonlinear Schrödinger equation on the half-line. For so-called linearizable boundary conditions, the method solves…
Analysis of stochastic Lanczos quadrature for spectrum approximation
Tyler Chen, Thomas Trogdon, Shashanka Ubaru
The cumulative empirical spectral measure (CESM) of a symmetric matrix is defined as the fraction of eigenvalues of…
Scattering and inverse scattering for the AKNS system: A rational function approach
Thomas Trogdon
We consider the use of rational basis functions to compute the scattering and inverse scattering transforms associated with the AKNS system. The proposed numerical forward scatteri…