## A pole-residue framework for optimal
*H*_{2} model reduction

### Harold Metz and Patrick Sheridan

In this paper, we describe our attempts to develop an algorithm for
solving the optimal *H*_{2} 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.