5 papers
Linear-cost Polyharmonic Spline Interpolation of Arbitrary Degree
Christopher J. Geoga, Michael O'Neil
We introduce a simple and performant approach for rapidly and accurately performing polyharmonic spline (PHS) interpolation using a combination of the fast multipole method (FMM) f…
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…
Fast Direct Solvers
Per-Gunnar Martinsson, Michael O'Neil
This survey describes a class of methods known as "fast direct solvers". These algorithms address the problem of solving a system of linear equations $\boldsymbol{Ax}=\boldsymbol{b…
Fast adaptive high-order integral equation methods for electromagnetic scattering from smooth perfect electric conductors
Felipe Vico, Leslie Greengard, Michael O'Neil +1
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise i…
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…