dc.contributor.advisor Xu, Hongguo dc.contributor.author Gu, Peidi dc.date.accessioned 2014-02-05T16:33:25Z dc.date.available 2014-02-05T16:33:25Z dc.date.issued 2013-12-31 dc.date.submitted 2013 dc.identifier.other http://dissertations.umi.com/ku:13159 dc.identifier.uri http://hdl.handle.net/1808/12977 dc.description.abstract The study introduces methods of finding eigenvalues for unitary matrices and pencils. Bunse-Gerstner and Elsner ([2]) proposed an algorithm of using the Schur parameter pencil to solve eigenproblems for unitary matrices and pencils. This thesis reviews the Schur parameter pencil algorithm. The method is divided into two phases: Reducing a unitary pencil to a Schur parameter form and QR-type shifted iteration. The algorithm is proved to be backward stable and more efficient than the standard QR/QZ algorithm. However, during the process of reduction, norms of vectors are frequently compared for numerical stability, which causes a lot of extra work for computations. Based on the idea in [8], we introduce a modified Schur parameter algorithm to avoid such frequent comparison. The modified algorithm is still divided into two phases similar to the one in [2]. A detailed reduction process and shifted iteration are described in this thesis. dc.format.extent 123 pages dc.language.iso en dc.publisher University of Kansas dc.rights This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author. dc.subject Mathematics dc.subject Eigenvalue dc.subject Givens matrix dc.subject Householder reflector dc.subject Iteration dc.subject Schur parameter form dc.subject Unitary matrix dc.title Finding Eigenvalues of Unitary Matrices dc.type Thesis dc.contributor.cmtemember Xu, Hongguo dc.contributor.cmtemember Tu, Xuemin dc.contributor.cmtemember Van Vleck, Erik dc.thesis.degreeDiscipline Mathematics dc.thesis.degreeLevel M.A. kusw.oastatus na kusw.oapolicy This item does not meet KU Open Access policy criteria. dc.rights.accessrights openAccess
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