dc.contributor.author | Jai, Zhongxiao | en_US |
dc.contributor.author | Stewart, G. W. | en_US |
dc.date.accessioned | 2004-05-31T22:55:48Z | |
dc.date.available | 2004-05-31T22:55:48Z | |
dc.date.created | 1999-01 | en_US |
dc.date.issued | 1999-01-29 | en_US |
dc.identifier.uri | http://hdl.handle.net/1903/993 | |
dc.description.abstract | This 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.extent | 150796 bytes | |
dc.format.mimetype | application/postscript | |
dc.language.iso | en_US | |
dc.relation.ispartofseries | UM Computer Science Department; CS-TR-3986 | en_US |
dc.relation.ispartofseries | UMIACS; UMIACS-TR-99-08 | en_US |
dc.title | On the Convergence of Ritz Values, Ritz Vectors, and Refined Ritz
Vectors\symbolmark | 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 |