8 papers
A recursive butterfly factorization with optimality guarantees
David Persson, Paul G. Beckman, Tyler Chen +2
We formalize a recursive format for representing a butterfly matrix. This new format naturally leads to a simple recursive algorithm for computing a quasi-optimal butterfly approxi…
A Butterfly-Accelerated Manifold Harmonic Transform
Paul G. Beckman, Samuel F. Potter, Michael O'Neil
The eigenfunctions of the Laplacian are a natural basis of functions for many tasks in computational mathematics. On the circle and sphere, the eigenfunctions are given by complex…
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +33
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…
Fast nonparametric spectral density estimation from irregularly sampled data
Christopher J. Geoga, Paul G. Beckman
We introduce a nonparametric spectral density estimator for continuous-time and continuous-space processes measured at fully irregular locations. Our estimator is constructed using…
A Nonuniform Fast Hankel Transform
Paul G. Beckman, Michael O'Neil
We describe a fast algorithm for computing discrete Hankel transforms of moderate orders from nonuniform points to nonuniform frequencies in operati…
Fast Adaptive Fourier Integration for Spectral Densities of Gaussian Processes
Paul G. Beckman, Christopher J. Geoga
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those use…
Scalable Computations for Nonstationary Gaussian Processes
Paul G. Beckman, Christopher J. Geoga, Michael L. Stein +1
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets…
A Shift Selection Strategy for Parallel Shift-Invert Spectrum Slicing in Symmetric Self-Consistent Eigenvalue Computation
David B. Williams-Young, Paul G. Beckman, Chao Yang
The central importance of large scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advance…