Type of Document Dissertation Author Wang, Yuan Author's Email Address firstname.lastname@example.org URN etd-81797-165028 Title Convergence and Boundedness of Probability-One Homotopies for Model Order Reduction Degree PhD Department Mathematics Advisory Committee
Advisor Name Title Watson, Layne T. Committee Chair Ball, Joseph A. Committee Member Herdman, Terry L. Committee Member Lin, Tao Committee Member Ribbens, Calvin J. Committee Member Rogers, Robert C. Committee Member Watson, Layne T. Committee Member Keywords
Date of Defense 1997-08-13 Availability unrestricted AbstractThe optimal model reduction problem 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.
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