A pole-residue framework for optimal H2 model reduction

Harold Metz and Patrick Sheridan

In this paper, we describe our attempts to develop an algorithm for solving the optimal H2 model reduction problem in a pole-residue framework using Newton's method. To this end, we convert the moment matching problem into a form where it requires finding the zero of a function. This function takes in the poles and residues of a reduced system as independent variables and is zero at the optimum reduced poles and residues. Newton's method is then applied to the function to numerically find the zero. We discovered that this problem does not seem well suited to be solved using Newton's method but converges much faster using the fixed point method of the iteratively corrected rational Krylov algorithm.