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
Keywords	BOUNDEDNESS CONVERGENCE
Date of Defense	1997-08-13
Availability	unrestricted
Abstract 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.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    ywang.pdf 696.10 Kb 00:03:13 00:01:39 00:01:27 00:00:43 00:00:03

If you have questions or technical problems, please Contact DLA.