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On the Convergence of Ritz Values, Ritz Vectors, and Refined Ritz Vectors\symbolmark

dc.contributor.authorJai, Zhongxiaoen_US
dc.contributor.authorStewart, G. W.en_US
dc.description.abstractThis paper concerns the Rayleigh--Ritz method for computing an approximation to an eigenpair $(\lambda, x)$ of a non-Hermitian matrix $A$. Given a subspace $\clw$ that contains an approximation to $x$, this method returns an approximation $(\mu, \tilde x)$ to $(\lambda, x)$. We establish four convergence results that hold as the deviation $\epsilon$ of $x$ from $\clw$ approaches zero. First, the Ritz value $\mu$ converges to $\lambda$. Second, if the residual $A\tilde x-\mu\tilde x$ approaches zero, then the Ritz vector $\tilde x$ converges to $x$. Third, we give a condition on the eigenvalues of the Rayleigh quotient from which the Ritz pair is computed that insures convergence of the Ritz vector. Finally, we show that certain unconditionally. (Also cross-referenced as UMIACS-TR-99-08)en_US
dc.format.extent150796 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3986en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-99-08en_US
dc.titleOn the Convergence of Ritz Values, Ritz Vectors, and Refined Ritz Vectors\symbolmarken_US
dc.typeTechnical Reporten_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.isAvailableAtUMIACS Technical Reportsen_US

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