dc.contributor.author Brennan, Michael C. en dc.date.accessioned 2018-08-28T08:00:45Z en dc.date.available 2018-08-28T08:00:45Z en dc.date.issued 2018-08-27 en dc.identifier.other vt_gsexam:16856 en dc.identifier.uri http://hdl.handle.net/10919/84924 en dc.description.abstract This 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.medium ETD en dc.publisher Virginia Tech en dc.rights In Copyright en dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ en dc.subject Nonlinear Eigenvalue Problems en dc.subject Contour Integration Methods en dc.subject Iterative Methods en dc.subject Dynamical Systems en dc.title Rational Interpolation Methods for Nonlinear Eigenvalue Problems en dc.type Thesis en dc.contributor.department Mathematics en dc.description.degree Master of Science en thesis.degree.name Master of Science en thesis.degree.level masters en thesis.degree.grantor Virginia Polytechnic Institute and State University en thesis.degree.discipline Mathematics en dc.contributor.committeechair Gugercin, Serkan en dc.contributor.committeemember Beattie, Christopher A. en dc.contributor.committeemember Embree, Mark Partick en
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