# A Generalization of Saad's Theorem on Rayleigh-Ritz Approximations

 dc.contributor.author Stewart, G. W. en_US dc.date.accessioned 2004-05-31T23:01:29Z dc.date.available 2004-05-31T23:01:29Z dc.date.created 1999-12 en_US dc.date.issued 2000-02-04 en_US dc.identifier.uri http://hdl.handle.net/1903/1050 dc.description.abstract Let $(\lambda,x)$ be an eigenpair of the Hermitian matrix $A$ of order $n$ and let $(\mu,u)$ be a Ritz pair from a subspace $\clk$ of $\comp^{2}$. Saad has given a simple inequality bounding $\sin\angle(x,u)$ in terms of $\sin\angle(x,\clk)$. In this note we show that this inequality can be extended to an equally simple inequality for eigenspaces of non-Hermitian matrices. (Also cross-referenced as UMIACS-TR-99-78) en_US dc.format.extent 104546 bytes dc.format.mimetype application/postscript dc.language.iso en_US dc.relation.ispartofseries UM Computer Science Department; CS-TR-4095 en_US dc.relation.ispartofseries UMIACS; UMIACS-TR-99-78 en_US dc.title A Generalization of Saad's Theorem on Rayleigh-Ritz Approximations en_US dc.type Technical Report en_US dc.relation.isAvailableAt Digital Repository at the University of Maryland en_US dc.relation.isAvailableAt University of Maryland (College Park, Md.) en_US dc.relation.isAvailableAt Tech Reports in Computer Science and Engineering en_US dc.relation.isAvailableAt UMIACS Technical Reports en_US
﻿