2 citations · 3 across the 3 of their papers we have counts for
6 papers
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…
A Probabilistic Analysis of the Neumann Series Iteration
Yiting Zhang, Thomas Trogdon
Given a random matrix A with eigenvalues between -1 and 1, we analyze the number of iterations needed to solve the linear equation (I-A)x=b with the Neumann series iteration. We gi…
Linear Dispersive Shocks
David Smith, Thomas Trogdon, Vishal Vasan
We present a linear dispersive partial differential equation which manifests a number of qualitative features of dispersive shocks, typically thought to occur only in nonlinear mod…
Stopping time signatures for some algorithms in cryptography
Percy Deift, Stephen D. Miller, Thomas Trogdon
We consider the normalized distribution of the overall running times of some cryptographic algorithms, and what information they reveal about the algorithms. Recent work of Deift,…
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.…