Lagrange rational interpolation and its applications to approximation of large-scale dynamical systems

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dc.contributor.advisorAntoulas, Athanasios C.en_US
dc.contributor.committeeMemberZhong, Linen_US
dc.contributor.committeeMemberEmbree, Marken_US
dc.creatorIonita, Antonioen_US
dc.date.accessioned2014-09-16T14:21:26Zen_US
dc.date.available2014-09-16T14:21:26Zen_US
dc.date.created2013-12en_US
dc.date.issued2013-11-06en_US
dc.date.submittedDecember 2013en_US
dc.date.updated2014-09-16T14:21:26Zen_US
dc.description.abstractWe present several new, efficient algorithms that extract low complexity models from frequency response measurements of large-scale dynamical systems. Our work is motivated by the fact that, in many applications, analytical models of a dynamical system are seldom available. Instead, we may only have access to its frequency response measurements. For example, for a system with multiple inputs and outputs, we may only have access to data sets of S-parameters. In this setting, our new approach extracts models that interpolate the given measurements. The extracted models have low complexity (or reduced order) and, thus, lead to short simulation times and low data storage requirements. The main tool used by our approach is Lagrange rational interpolation -- a generalization of the classic result of Lagrange polynomial interpolation. We present an in-depth look at Lagrange rational interpolation and provide several new insights and simplified proofs. This analysis leads to new algorithms that rely on the singular value decomposition (SVD) of the Loewner matrix pencil formed directly from the measurements. We show several new results on rational interpolation for measurements of linear, bi-linear and quadratic-linear systems. Furthermore, we generalize these results to parametrized measurements, that is, we show how to interpolate frequency response measurements that depend on parameters. We showcase this new approach through a series of relevant numerical examples such as n-port systems and parametrized partial differential equations.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationIonita, Antonio. "Lagrange rational interpolation and its applications to approximation of large-scale dynamical systems." (2013) Diss., Rice University. <a href="https://hdl.handle.net/1911/77180">https://hdl.handle.net/1911/77180</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/77180en_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.subjectRational interpolationen_US
dc.subjectLagrange basisen_US
dc.subjectLoewner matrixen_US
dc.subjectBilinear systemsen_US
dc.subjectQuadratic systemsen_US
dc.subjectSystem identificationen_US
dc.subjectFrequency response measurementsen_US
dc.subjectS-parametersen_US
dc.subjectY-parametersen_US
dc.subjectRational approximationen_US
dc.subjectBest rational approximationen_US
dc.subjectRemez iterationen_US
dc.subjectModel order reductionen_US
dc.subjectApproximation of large-scale dynamical systemsen_US
dc.subjectParametrized systemsen_US
dc.titleLagrange rational interpolation and its applications to approximation of large-scale dynamical systemsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentElectrical and Computer Engineeringen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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