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05/23/2023
On the convergence of spectral methods involving non-compact operators
Motivated by Fredholm theory, we develop a framework to establish the co...
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04/11/2023
Computing the Tracy-Widom distribution for arbitrary β>0
We compute the Tracy-Widom distribution describing the asymptotic distri...
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03/03/2023
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginibre matrices
We study the GMRES algorithm applied to linear systems of equations invo...
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02/28/2023
Stability of the Lanczos algorithm on matrices with regular spectral distributions
We study the stability of the Lanczos algorithm run on problems whose ei...
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02/24/2023
A Riemann–Hilbert approach to computing the inverse spectral map for measures supported on disjoint intervals
We develop a numerical method for computing with orthogonal polynomials ...
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01/13/2023
An artificially-damped Fourier method for dispersive evolution equations
Computing solutions to partial differential equations using the fast Fou...
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04/30/2022
Computation of Large-Genus Solutions of the Korteweg-de Vries Equation
We consider the numerical computation of finite-genus solutions of the K...
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04/05/2022
Randomized matrix-free quadrature for spectrum and spectral sum approximation
We study randomized matrix-free quadrature algorithms for spectrum and s...
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03/29/2022
Growth factors of random butterfly matrices and the stability of avoiding pivoting
Random butterfly matrices were introduced by Parker in 1995 to remove th...
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12/23/2021
A Riemann–Hilbert approach to the perturbation theory for orthogonal polynomials: Applications to numerical linear algebra and random matrix theory
We establish a new perturbation theory for orthogonal polynomials using ...
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06/25/2021
The conjugate gradient algorithm on a general class of spiked covariance matrices
We consider the conjugate gradient algorithm applied to a general class ...
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06/11/2021
The Numerical Unified Transform Method for the Nonlinear Schrödinger equation on the half-line
We implement the Numerical Unified Transform Method to solve the Nonline...
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05/13/2021
Analysis of stochastic Lanczos quadrature for spectrum approximation
The cumulative empirical spectral measure (CESM) Φ[𝐀] : ℝ→ [0,1] of a n×...
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03/17/2021
Scattering and inverse scattering for the AKNS system: A rational function approach
We consider the use of rational basis functions to compute the scatterin...
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07/01/2020
Universality for the conjugate gradient and MINRES algorithms on sample covariance matrices
We present a probabilistic analysis of two Krylov subspace methods for s...
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06/10/2020
The Numerical Unified Transform Method for Initial-boundary Value Problems on the Half-line
We implement the Unified Transform Method of Fokas as a numerical method...
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05/21/2019
Stopping time signatures for some algorithms in cryptography
We consider the normalized distribution of the overall running times of ...
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01/25/2019
The conjugate gradient algorithm on well-conditioned Wishart matrices is almost deteriministic
We prove that the number of iterations required to solve a random positi...
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11/19/2015