4 papers
On the construction of scattering matrices for irregular or elongated enclosures using Green's representation formula
Carlos Borges, Leslie Greengard, Michael O'Neil +1
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing…
A Fast Compensated Algorithm for Computing Givens Rotations
Carlos F. Borges
We develop a very simple compensated scheme for computing very accurate Givens rotations. The approach is significantly more straightforward than the one in \cite{borges2021fast},…
Random walks in frequency and the reconstruction of obstacles with cavities from multi-frequency data
Travis Askham, Carlos Borges, Jeremy Hoskins +1
Inverse obstacle scattering is the recovery of an obstacle boundary from the scattering data produced by incident waves. This shape recovery can be done by iteratively solving a PD…
A Correctly Rounded Newton Step for the Reciprocal Square Root
Carlos F. Borges
The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example \cite{Moroz,863046,863031} and the references therein). A comm…