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Convergence and Boundedness of Probability-One Homotopies for Model Order Reduction

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dc.contributor.authorWang, Yuanen
dc.contributor.committeechairWatson, Layne T.en
dc.contributor.committeememberLin, Taoen
dc.contributor.committeememberRibbens, Calvin J.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.committeememberRogers, Robert C.en
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.committeememberWatson, Layne T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:22:34Zen
dc.date.adate1997-09-18en
dc.date.available2014-03-14T20:22:34Zen
dc.date.issued1997-08-13en
dc.date.rdate1997-09-18en
dc.date.sdate1997-08-13en
dc.description.abstractThe 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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-81797-165028en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-81797-165028/en
dc.identifier.urihttp://hdl.handle.net/10919/30716en
dc.publisherVirginia Techen
dc.relation.haspartywang.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectBoundednessen
dc.subjectConvergenceen
dc.titleConvergence and Boundedness of Probability-One Homotopies for Model Order Reductionen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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