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dc.contributor.advisor Embree, Mark
dc.creatorCarden, Russell
dc.date.accessioned 2011-07-25T01:38:32Z
dc.date.available 2011-07-25T01:38:32Z
dc.date.issued 2009
dc.identifier.citation Carden, Russell. "Ritz values and Arnoldi convergence for nonsymmetric matrices." (2009) Master’s Thesis, Rice University. https://hdl.handle.net/1911/61834.
dc.identifier.urihttps://hdl.handle.net/1911/61834
dc.description.abstract The restarted Arnoldi method, useful for determining a few desired eigenvalues of a matrix, employs shifts to refine eigenvalue estimates. In the symmetric case, using selected Ritz values as shifts produces convergence due to interlacing. For nonsymmetric matrices the behavior of Ritz values is insufficiently understood, and hence no satisfactory general convergence theory exists. Towards developing such a theory, this work demonstrates that Ritz values of nonsymmetric matrices can obey certain geometric constraints, as illustrated through careful analysis of Jordan blocks. By constructing conditions for localizing the Ritz values of a matrix with one simple normal wanted eigenvalue, this work develops sufficient conditions that guarantee convergence of the restarted Arnoldi method with exact shifts. As Ritz values are the basis for many iterative methods for determining eigenvalues and solving linear systems, an understanding of Ritz value behavior for nonsymmetric matrices has the potential to inform a broad range of analysis.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
dc.title Ritz values and Arnoldi convergence for nonsymmetric matrices
dc.type Thesis
dc.type.material Text
thesis.degree.department Mathematical Sciences
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Masters
thesis.degree.name Master of Arts
dc.identifier.callno THESIS MATH. SCI. 2009 CARDEN


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