Computing optimal Hankel norm approximations of large-scale systems

We discuss an efficient algorithm for optimal Hankel norm approximation of large-scale systems and an implementation which allows to reduce models of order up to O(10⁴) using parallel computing techniques. The major computational tasks in this approach are the computation of a minimal balanced realization, involving the solution of two Lyapunov equations, and the additive decomposition of a transfer function via block diagonalization. We will illustrate that these computational tasks can all be performed using iterative schemes for the matrix sign function. Numerical experiments on a cluster of Linux PCs show the efficiency of our methods.