Soundness is a major objective for verification tools. Methods
that use exact arithmetic or symbolic representations are often prohibitively
slow and do not scale past small examples. We propose the
use of numerical
oating-point computations to improve performance
combined with an interval analysis to ensure soundness in reach-set computations
for numerical dynamical models. Since the interval analysis
cannot provide exact answers we reason about over-approximations of
the reachable sets that are guaranteed to contain the true solution of
the problem. Our theory is implemented in a numerical algorithm for
Abstract Acceleration in a tool called Axelerator. Experimental results
show a large increase in performance while maintaining soundness of
reachability results
