Contragredient Transformations Applied to the Optimal Projection Equations

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dc.contributor.authorZigic, Draganen
dc.contributor.authorWatson, Layne T.en
dc.contributor.authorBeattie, Christopher A.en
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2013-06-19T14:37:06Zen
dc.date.available2013-06-19T14:37:06Zen
dc.date.issued1992en
dc.description.abstractThe optimal projection approach to solving the H2 reduced order model problem produces two coupled, highly nonlinear matrix equations with rank conditions as constraints. It is not obvious from their original form how they can be differentiated and how some algorithm for solving nonlinear equations can be applied to them. A contragredient transformation, a transformation which simultaneously diagonalizes two symmetric positive semi-definite matrices, is used to transform the equations into forms suitable for algorithms for solving nonlinear problems. Three different forms of the equations obtained using contragredient transformations are given. An SVD-based algorithm for the contragredient transformation and a homotopy algorithm for the transformed equations are given, together with a numerical example.en
dc.format.mimetypeapplication/pdfen
dc.identifierhttp://eprints.cs.vt.edu/archive/00000308/en
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00000308/01/TR-92-28.pdfen
dc.identifier.trnumberTR-92-28en
dc.identifier.urihttp://hdl.handle.net/10919/19645en
dc.language.isoenen
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen
dc.relation.ispartofHistorical Collection(Till Dec 2001)en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleContragredient Transformations Applied to the Optimal Projection Equationsen
dc.typeTechnical reporten
dc.type.dcmitypeTexten

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