204 citations · 675 across the 44 of their papers we have counts for
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Efficient high-order accurate Fresnel diffraction via areal quadrature and the nonuniform FFT
Alex H. Barnett
We present a fast algorithm for computing the diffracted field from arbitrary binary (sharp-edged) planar apertures and occulters in the scalar Fresnel approximation, for up to mod…
How exponentially ill-conditioned are contiguous submatrices of the Fourier matrix?
Alex H. Barnett
We show that the condition number of any cyclically contiguous submatrix of the discrete Fourier transform (DFT) matrix is at least $$ \exp \left( \fracπ{2}…
A high-order integral equation-based solver for the time-dependent Schrodinger equation
Jason Kaye, Alex Barnett, Leslie Greengard
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We…
Aliasing error of the exp kernel in the nonuniform fast Fourier transform
A. H. Barnett
The most popular algorithm for the nonuniform fast Fourier transform (NUFFT) uses the dilation of a kernel to spread (or interpolate) between given nonuniform points and a unif…