ATTENTION: The software behind KU ScholarWorks is being upgraded to a new version. Starting July 15th, users will not be able to log in to the system, add items, nor make any changes until the new version is in place at the end of July. Searching for articles and opening files will continue to work while the system is being updated.
If you have any questions, please contact Marianne Reed at mreed@ku.edu .
Finding Eigenvalues of Unitary Matrices
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. | |
kusw.bibid | 8086497 | |
kusw.bibid | 8086497 | |
dc.rights.accessrights | openAccess |
Files in this item
This item appears in the following Collection(s)
-
Mathematics Dissertations and Theses [179]
-
Theses [4088]