a dynamic algorithm for approximate flow computations
In this paper we consider the problem of approximating the set of states reachable within a time bound T in a linear dynamical system, to within a given error bound ? . Fixing a degree d , our algorithm divides the interval [0, T ] into sub-intervals of not necessarily equal size, such that a polynomial of degree d approximates the actual flow to within an error bound of ? , and approximates the reach set within each sub-interval by the polynomial tube. Our experimental evaluation of the algorithm when the degree d is fixed to be either 1 or 2, shows that the approach is promising, as it scales to large dimensional dynamical systems, and performs better than previous approaches that divided the interval [0, T ] evenly into sub-intervals.
approximation linear dynamical systems post computation