Numerical methods for large scale matrix equations with applications in LTI system model reduction

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dc.contributor.advisorSorensen, Danny C.en_US
dc.creatorZhou, Yunkaien_US
dc.date.accessioned2009-06-04T08:06:31Zen_US
dc.date.available2009-06-04T08:06:31Zen_US
dc.date.issued2002en_US
dc.description.abstractLTI (Linear Time Invariant) systems arise frequently in different branches of engineering. This thesis mainly concerns the properties and numerical methods for large scale matrix equations related to LTI systems, the final goal is model reduction. Due to the importance of small to medium scale matrix equations, we firstly made formulation improvements to the two standard direct methods (the Bartels-Stewart's method and the Hammarling's method) for Sylvester and Lyapunov equations. Numerical evidence and flop counts show the better performance of our modified formulations. The low rank solution property of large scale Lyapunov equations is the basis for any algorithm that computes low rank approximate solutions. We study the eigendecay rate of the solution since eigen-decay rate is closely related to the low rank solution property. New eigen-decay rate bounds and estimated rates are established for general nonsymmetric Lyapunov equation. Connections between the solution of Lyapunov equation and some special matrices are discussed, which further reveal different properties of the solution. We also present new bounds on the conditioning of Lyapunov operator. Finally, we develop an AISIAD (Approximate Implicit Subspace Iteration with Alternating Directions) framework for model reduction. Two new approaches within this framework are constructed. The efficiency of these approaches are demonstrated by numerical results.en_US
dc.format.extent171 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. SCI. 2002 ZHOUen_US
dc.identifier.citationZhou, Yunkai. "Numerical methods for large scale matrix equations with applications in LTI system model reduction." (2002) Diss., Rice University. <a href="https://hdl.handle.net/1911/18160">https://hdl.handle.net/1911/18160</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/18160en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectApplied mechanicsen_US
dc.subjectElectronicsen_US
dc.subjectElectrical engineeringen_US
dc.titleNumerical methods for large scale matrix equations with applications in LTI system model reductionen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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