Pradeep Misra (Advisor), Luther Palmer III (Committee Member), Xiaodong Zhang (Committee Member)
Master of Science in Engineering (MSEgr)
Considerable literature exists in linear algebra to solve the generalized eigenvalue, eigenvector problem (F − [lambda]G)v = 0 where F, G 2 Rs×s, are square matrices. However, a number of applications lend themselves to the case whereF, G 2 Rs×, and s ≠ t. The existing methods cannot be used for such non-square cases. This research explores structural decomposition of a matrix pencil (F − [lambda]G), s 6≠ t to compute finite values of [lambda] for which rank (F − [lambda]G) < min(s, t). Moreover, from the decomposition of the matrix pencil, information about the order of [lambda] at infinity, the Kronecker row and column indices of a matrix pencil can also be extracted. Equally important is the computation of non-zero vectors w 2 R1×s and v 2 Rt×1 corresponding to each finite value of [lambda], such that w(F - [lambda] G) = 0 and (F - [lambda]G)v = 0. Algorithms are developed for the computation of lambda, w, and v using numerically efficient techniques. Proposed algorithms are applied to problems encountered in system theory and illustrated by means of numerical examples.
Department or Program
Department of Electrical Engineering
Year Degree Awarded
Copyright 2017, all rights reserved. My ETD will be available under the "Fair Use" terms of copyright law.