  Prony's method is a standard tool exploited for solving many imaging and data
analysis problems that result in parameter identification in sparse exponential
sums $$f(k)=\sum_{j=1}^{T}c_{j}e^{-2\pi i\langle t_{j},k\rangle},\quad k\in
\mathbb{Z}^{d},$$ where the parameters are pairwise different $\{
t_{j}\}_{j=1}^{M}\subset [0,1)^{d}$, and $\{ c_{j}\}_{j=1}^{M}\subset
\mathbb{C}\setminus \{ 0\}$ are nonzero. The focus of our investigation is on a
Prony's method variant based on a multivariate matrix pencil approach. The
method constructs matrices $S_{1}$, \ldots , $S_{d}$ from the sampling values,
and their simultaneous diagonalization yields the parameters $\{
t_{j}\}_{j=1}^{M}$. The parameters $\{ c_{j}\}_{j=1}^{M}$ are computed as the
solution of an linear least squares problem, where the matrix of the problem is
determined by $\{ t_{j}\}_{j=1}^{M}$. Since the method involves independent
generation and manipulation of certain number of matrices, there is intrinsic
capacity for parallelization of the whole computation process on several
levels. Hence, we propose parallel version of the Prony's method in order to
increase its efficiency. The tasks concerning generation of matrices is divided
among GPU's block of threads and CPU, where heavier load is put on the GPU.
From the algorithmic point of view, the CPU is dedicated to the more complex
tasks. With careful choice of algorithms solving the subtasks, the load between
CPU and GPU is balanced. Besides the parallelization techniques, we are also
concerned with some numerical issues, and we provide detailed numerical
analysis of the method in case of noisy input data. Finally, we performed a set
of numerical tests which confirm superior efficiency of the parallel algorithm
and consistency of the forward error with the results of numerical analysis.
