5 papers · 1 filter
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…
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…
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…