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dc.contributor.advisorXu, Hongguo
dc.contributor.authorGu, Peidi
dc.date.accessioned2014-02-05T16:33:25Z
dc.date.available2014-02-05T16:33:25Z
dc.date.issued2013-12-31
dc.date.submitted2013
dc.identifier.otherhttp://dissertations.umi.com/ku:13159
dc.identifier.urihttp://hdl.handle.net/1808/12977
dc.description.abstractThe 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.extent123 pages
dc.language.isoen
dc.publisherUniversity of Kansas
dc.rightsThis item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
dc.subjectMathematics
dc.subjectEigenvalue
dc.subjectGivens matrix
dc.subjectHouseholder reflector
dc.subjectIteration
dc.subjectSchur parameter form
dc.subjectUnitary matrix
dc.titleFinding Eigenvalues of Unitary Matrices
dc.typeThesis
dc.contributor.cmtememberXu, Hongguo
dc.contributor.cmtememberTu, Xuemin
dc.contributor.cmtememberVan Vleck, Erik
dc.thesis.degreeDisciplineMathematics
dc.thesis.degreeLevelM.A.
kusw.oastatusna
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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