@article {17690,
	title = {Analysis of the Residual Arnoldi Method},
	volume = {UMIACS-TR-2007-45},
	year = {2007},
	month = {2007/10/15/},
	institution = {Instititue for Advanced Computer Studies, Univ of Maryland, College Park},
	abstract = {The Arnoldi method generates a nested squences of orthonormal bases$U_{1},U_{2}, \ldots$ by orthonormalizing $Au_{k}$ against $U_{k}$.
Frequently these bases contain increasingly accurate approximations of
eigenparis from the periphery of the spectrum of $A$.  However, the
convergence of these approximations stagnates if $u_{k}$ is
contaminated by error.  It has been observed that if one chooses a
Rayleigh--Ritz approximation $(\mu_{k}, z_{k})$ to a chosen target
eigenpair $(\lambda, x)$ and orthonormalizes the residual $Az_{k -
}\mu_{k} z_{k}$, the approximations to $x$ (but not the other
eigenvectors) continue to converge, even when the residual is
contaminated by error.  The same is true of the shift-invert variant
of Arnoldi{\textquoteright}s method.  In this paper we give a mathematical analysis
of these new methods.
},
	keywords = {Technical Report},
	url = {http://drum.lib.umd.edu/handle/1903/7428},
	author = {Lee,Che-Rung and Stewart, G.W.}
}
