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Analysis of the Residual Arnoldi Method

dc.contributor.authorLee, Che-Rung
dc.contributor.authorStewart, G. W.
dc.date.accessioned2007-10-15T17:23:08Z
dc.date.available2007-10-15T17:23:08Z
dc.date.issued2007-10-15
dc.identifier.urihttp://hdl.handle.net/1903/7428
dc.description.abstractThe 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's method. In this paper we give a mathematical analysis of these new methods.en
dc.format.extent318799 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_USen
dc.relation.ispartofseriesUM Computer Science Departmenten
dc.relation.ispartofseriesCS-TR-4890en
dc.relation.ispartofseriesUMIACSen
dc.relation.ispartofseriesUMIACS-TR-2007-45en
dc.titleAnalysis of the Residual Arnoldi Methoden
dc.typeTechnical Reporten


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