| Popis: |
The H 2 optimal model reduction problem, i.e., the problem of approximating a higher order dynamical system by a lower order one so that a model reduction criterion is minimized, is of significant importance and is under intense study. Several earlier attempts to apply homotopy methods to the H 2 optimal model order reduction problem were not entirely satisfactory. Richter devised a homotopy approach which only estimated certain crucial partial derivatives and employed relatively crude curve tracking techniques. Žigic, Bernstein, Collins, Richter, and Watson formulated the problem so that numerical linear algebra techniques could be used to explicitly calculate partial derivatives, and employed sophisticated homotopy curve tracking algorithms, but the number of variables made large problems intractable. We propose here several ways to reduce the dimension of the homotopy map so that large problems are computationally feasible. |
