Scholarly
    Communications Project


Document Type:Dissertation
Name:Yuan Wang
Email address:y.wang@larc.nasa.gov
URN:1997/00212
Title:CONVERGENCE AND BOUNDEDNESS OF PROBABILITY-ONE HOMOTOPIES FOR MODEL ORDER REDUCTION
Degree:Doctor of Philosophy
Department:Mathematics
Committee Chair: Layne T. Watson
Chair's email:ltw@cs.vt.edu
Committee Members:Layne T. Watson
Joseph Ball
Robert C. Rogers
Terry Herdman
Calvin J. Ribbens
Tao Lin
Keywords:CONVERGENCE, BOUNDEDNESS
Date of defense:Aug. 13, 1997
Availability:Release the entire work for Virginia Tech access only.
After one year release worldwide only with written permission of the student and the advisory committee chair.

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.

List of Attached Files

ETD.TGZ ywang.pdf


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