2 research outputs found
Transient Response in Matrix Discrete-Time Linear Systems
The behavior of trajectories of multidimensional linear discrete-time systems with
nonzero initial conditions is considered in two cases as follows. The first case is the systems
with infinite degree of stability (the processes of a finite duration); the second case is the stable
systems with a spectral radius close to 1. It is demonstrated that in both cases, large deviations
of the trajectories from the equilibrium may occur. These results are applied to accelerated
unconstrained optimization methods (such as the Heavy-ball method) for explaining the nonmonotonic
behavior of the methods, which is observed in practice.Russian Science Foundation, project no. 16-11-1001