Iterative computation of L2-sensitivity optimal realizations

The authors study convergence properties of solutions to two types of nonlinear matrix difference equations which are created as a means to solving iteratively a class of nonlinear algebraic matrix equations. Based on the general convergence result, they propose several iterative algorithms to compute L²-sensitivity optimal realizations as well as Euclidean norm balancing realizations of a given linear system. These algorithms turn out to be far more practical for digital computer implementation than the gradient flows previously proposed and have a locally exponential convergence property