Effect of initial system on homotopy methods for the H2 reduced order model problem

The effects of different initial systems on the efficiency of homotopy methods for solving the H₂ reduced order model problem was considered. Two major strategies for improving the efficiency are examined. One strategy, which involves solving the initial problem, usually leads to better results, but there is no known method to solve the initial problem for all or a majority of the initial systems. Another strategy, which considers constructing the initial system such that its eigenvalues resemble the eigenvalues of the final system, in some cases is more efficient. Also, a hybrid that combines the two previous strategies is considered. Finally, it is shown by an example that an unwise choice of the initial system can lead to a very inefficient algorithm