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dc.contributor.advisor Antoulas, Athanasios C.
dc.creatorIonita, Antonio
dc.date.accessioned 2014-09-16T14:21:26Z
dc.date.available 2014-09-16T14:21:26Z
dc.date.created 2013-12
dc.date.issued 2013-11-06
dc.date.submitted December 2013
dc.identifier.citation Ionita, Antonio. "Lagrange rational interpolation and its applications to approximation of large-scale dynamical systems." (2013) Diss., Rice University. https://hdl.handle.net/1911/77180.
dc.identifier.urihttps://hdl.handle.net/1911/77180
dc.description.abstract We 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.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectRational interpolation
Lagrange basis
Loewner matrix
Bilinear systems
Quadratic systems
System identification
Frequency response measurements
S-parameters
Y-parameters
Rational approximation
Best rational approximation
Remez iteration
Model order reduction
Approximation of large-scale dynamical systems
Parametrized systems
dc.title Lagrange rational interpolation and its applications to approximation of large-scale dynamical systems
dc.contributor.committeeMember Zhong, Lin
dc.contributor.committeeMember Embree, Mark
dc.date.updated 2014-09-16T14:21:26Z
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Electrical and Computer Engineering
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy


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