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dc.contributor.advisorTsatsomeros, Michael
dc.creatorCameron, Thomas R.
dc.date.accessioned2017-06-19T17:42:02Z
dc.date.available2017-06-19T17:42:02Z
dc.date.issued2016
dc.identifier.urihttp://hdl.handle.net/2376/12050
dc.descriptionThesis (Ph.D.), Mathematics, Washington State Universityen_US
dc.description.abstractIn this dissertation we focus on root-finding methods, such as Laguerre's method, for solving the polynomial eigenvalue problem. Serious consideration is given to the initial conditions and stopping criteria. Cost efficient and accurate strategies for computing eigenvectors, backward error, and condition estimates are given. Applications for both Hessenberg and tridiagonal structure are provided, and it shown that significant computational savings can be made from both structures. Surprising results concerning the spectral bounds for unitary matrix polynomials are presented. In addition, a constructive proof is provided for the result that every square matrix polynomial can be reduced to an upper Hessenberg matrix whose entries are rational functions and in special cases polynomials. The determinant of the matrix polynomial is preserved under this transformation, and sufficient conditions are provided for which the Smith form is preserved.en_US
dc.description.sponsorshipWashington State University, Mathematicsen_US
dc.languageEnglish
dc.rightsIn copyright
dc.rightsPublicly accessible
dc.rightsopenAccess
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.rights.urihttp://www.ndltd.org/standards/metadata
dc.rights.urihttp://purl.org/eprint/accessRights/OpenAccess
dc.subjectMathematics
dc.subjectHessenberg form
dc.subjectLaguerre's method
dc.subjectmatrix polynomials
dc.subjectpolynomial eigenvalue problem
dc.subjectroot finding algorithm
dc.subjectUnitary matrix polynomials
dc.titleOn the computation of eigenvalues, spectral bounds, and Hessenberg form for matrix polynomials
dc.typeElectronic Thesis or Dissertation


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