On the Convergence of a New Rayleigh Quotient Method with Applications to Large Eigenproblems

dc.contributor.authorO'Leary, D. P.en_US
dc.contributor.authorStewart, G. W.en_US
dc.date.accessioned2004-05-31T21:07:09Z
dc.date.available2004-05-31T21:07:09Z
dc.date.created1997-10en_US
dc.date.issued1998-10-15en_US
dc.description.abstractIn this paper we propose a variant of the Rayleigh quotient method to compute an eigenvalue and corresponding eigenvectors of a matrix. It is based on the observation that eigenvectors of a matrix with eigenvalue zero are also singular vectors corresponding to zero singular values. Instead of computing eigenvector approximations by the inverse power method, we take them to be the singular vectors corresponding to the smallest singular value of the shifted matrix. If these singular vectors are computed exactly the method is quadratically convergent. However, exact singular vectors are not required for convergence, and the resulting method combined with Golub--Kahan--Krylov bidiagonalization looks promising for enhancement/refinement methods for large eigenvalue problems. (Also cross-referenced as UMIACS-97-74)en_US
dc.format.extent135739 bytes
dc.format.mimetypeapplication/postscript
dc.identifier.urihttp://hdl.handle.net/1903/485
dc.language.isoen_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtComputer Science Department Technical Reportsen_US
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3839en_US
dc.titleOn the Convergence of a New Rayleigh Quotient Method with Applications to Large Eigenproblemsen_US
dc.typeTechnical Reporten_US

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