  Moving scientific computation from high-performance computing (HPC) and cloud
computing (CC) environments to devices on the edge, i.e., physically near
instruments of interest, has received tremendous interest in recent years. Such
edge computing environments can operate on data in-situ, offering enticing
benefits over data aggregation to HPC and CC facilities that include avoiding
costs of transmission, increased data privacy, and real-time data analysis.
Because of the inherent unreliability of edge computing environments, new fault
tolerant approaches must be developed before the benefits of edge computing can
be realized. Motivated by algorithm-based fault tolerance, a variant of the
asynchronous Jacobi (ASJ) method is developed that achieves resilience to data
corruption by rejecting solution approximations from neighbor devices according
to a bound derived from convergence theory. Numerical results on a
two-dimensional Poisson problem show the new rejection criterion, along with a
novel approximation to the shortest path length on which the criterion depends,
restores convergence for the ASJ variant in the presence of certain types data
corruption. Numerical results are obtained for when the singular values in the
analytic bound are approximated. A linear system with a more dense sparsity
pattern is also explored. All results indicate that successful resilience to
data corruption depends on whether the bound tightens fast enough to reject
corrupted data before the iteration evolution deviates significantly from that
predicted by the convergence theory defining the bound. This observation
generalizes to future work on algorithm-based fault tolerance for other
asynchronous algorithms, including upcoming approaches that leverage Krylov
subspaces.
