4 citations · 7 across the 6 of their papers we have counts for
8 papers
A high-order regularized delta-Chebyshev method for computing spectral densities
Jinjing Yi, Daniel Massatt, Andrew Horning +3
We introduce a numerical method for computing spectral densities, and apply it to the evaluation of the local density of states (LDOS) of sparse Hamiltonians derived from tight-bin…
An Introductory Guide to Koopman Learning
Matthew J. Colbrook, Zlatko Drmač, Andrew Horning
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges.…
Quadrature formulas from rational approximations
Andrew Horning, Lloyd N. Trefethen
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approxim…
Computing Generalized Eigenfunctions in Rigged Hilbert Spaces
Matthew J. Colbrook, Andrew Horning, Tianyiwa Xie
We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach…
A family of high-order accurate contour integral methods for strongly continuous semigroups
Andrew Horning, Adam R. Gerlach
Exponential integrators based on contour integral representations lead to powerful numerical solvers for a variety of ODEs, PDEs, and other time-evolution equations. They are embar…
Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators
Matthew J. Colbrook, Catherine Drysdale, Andrew Horning
We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolutio…
ContHutch++: Stochastic trace estimation for implicit integral operators
Jennifer Zvonek, Andrew Horning, Alex Townsend
Hutchinson's estimator is a randomized algorithm that computes an -approximation to the trace of any positive semidefinite matrix using matrix-vector produc…
The limiting distribution of a random variable transformed by Chebyshev Polynomials
Javier Chico Vazquez, Andrew J. Horning
In this paper we present the result of successively applying a Chebyshev polynomial to a continuous random variable. In particular we show that under mild assumptions the limiting…