Show simple item record

dc.contributor.authorBrennan, Michael C.en
dc.date.accessioned2018-08-28T08:00:45Zen
dc.date.available2018-08-28T08:00:45Zen
dc.date.issued2018-08-27en
dc.identifier.othervt_gsexam:16856en
dc.identifier.urihttp://hdl.handle.net/10919/84924en
dc.description.abstractThis thesis investigates the numerical treatment of nonlinear eigenvalue problems. These problems are defined by the condition $T(lambda) v = boldsymbol{0}$, with $T: C to C^{n times n}$, where we seek to compute the scalar-vector pairs, $lambda in C$ and nonzero $ v in C^{n}$. The first contribution of this work connects recent contour integration methods to the theory and practice of system identification. This observation leads us to explore rational interpolation for system realization, producing a Loewner matrix contour integration technique. The second development of this work studies the application of rational interpolation to the function $T(z)^{-1}$, where we use the poles of this interpolant to approximate the eigenvalues of $T$. We then expand this idea to several iterative methods, where at each step the approximate eigenvalues are taken as new interpolation points. We show that the case where one interpolation point is used is theoretically equivalent to Newton's method for a particular scalar function.en
dc.format.mediumETDen
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectNonlinear Eigenvalue Problemsen
dc.subjectContour Integration Methodsen
dc.subjectIterative Methodsen
dc.subjectDynamical Systemsen
dc.titleRational Interpolation Methods for Nonlinear Eigenvalue Problemsen
dc.typeThesisen
dc.contributor.departmentMathematicsen
dc.description.degreeMaster of Scienceen
thesis.degree.nameMaster of Scienceen
thesis.degree.levelmastersen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.disciplineMathematicsen
dc.contributor.committeechairGugercin, Serkanen
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.committeememberEmbree, Mark Particken


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record