The optimal model reduction problem, whether formulated in the H² or H<sup>∞</sup> norm frameworks, is an inherently nonconvex problem and thus provides a nontrivial computational challenge. This study systematically examines the requirements of probability-one homotopy methods to guarantee global convergence. Homotopy algorithms for nonlinear systems of equations construct a continuous family of systems, and solve the given system by tracking the continuous curve of solutions to the family. The main emphasis is on guaranteeing transversality for several homotopy maps based upon the pseudogramian formulation of the optimal projection equations and variations based upon canonical forms. These results are essential to the probability-one homotopy approach by guaranteeing good numerical properties in the computational implementation of the homotopy algorithms. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/30716 |
| Date | 18 September 1997 |
| Creators | Wang, Yuan |
| Contributors | Mathematics, Watson, Layne T., Lin, Tao, Ribbens, Calvin J., Herdman, Terry L., Rogers, Robert C., Ball, Joseph A., Watson, Layne T. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | ywang.pdf |
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