7 citations · 10 across the 7 of their papers we have counts for
6 papers · 1 filter
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…
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…
Universality for the conjugate gradient and MINRES algorithms on sample covariance matrices
Elliot Paquette, Thomas Trogdon
We present a probabilistic analysis of two Krylov subspace methods for solving linear systems. We prove a central limit theorem for norms of the residual vectors that are produced…
The Numerical Unified Transform Method for Initial-boundary Value Problems on the Half-line
Bernard Deconinck, Thomas Trogdon, Xin Yang
We implement the Unified Transform Method of Fokas as a numerical method to solve linear partial differential equations on the half-line. The method computes the solution at any x…
The conjugate gradient algorithm on well-conditioned Wishart matrices is almost deterministic
Percy Deift, Thomas Trogdon
We prove that the number of iterations required to solve a random positive definite linear system with the conjugate gradient algorithm is almost deterministic for large matrices.…