Analysis Seminar: Andrei Osipov (Yale) "On the evaluation of sums of periodic Gaussians"

Wed, 20/03/201912:00-13:00
Ross 70
On the evaluation of sums of periodic Gaussians
Discrete sums of the form
$\sum_{k=1}^N q_k \cdot \exp\left( -\frac{t – s_k}{2 \cdot \sigma^2} \right)$
where $\sigma>0$ and $q_1, \dots, q_N$ are real numbers and
$s_1, \dots, s_N$ and $t$ are vectors in $R^d$,
are frequently encountered in numerical computations across a variety of fields.
We describe an algorithm for the evaluation of such sums under periodic boundary conditions, provide a rigorous error analysis, and discuss its implications on the computational cost and choice of parameters.
While the algorithm itself was introduced before (and is closely related
to a class of algorithms for the evaluation of non-uniform discrete Fourier Transforms), the error analysis and its consequences appear to be novel.
We illustrate our results via numerical experiments.