Title page for ETD etd-81797-165028

Type of Document Dissertation
Author Wang, Yuan
Author's Email Address y.wang@larc.nasa.gov
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
Date of Defense 1997-08-13
Availability unrestricted
The 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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