Show simple item record

Analysis of the Residual Arnoldi Method

dc.contributor.authorLee, Che-Rung
dc.contributor.authorStewart, G. W.
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.relation.ispartofseriesUM Computer Science Departmenten
dc.titleAnalysis of the Residual Arnoldi Methoden
dc.typeTechnical Reporten

Files in this item


This item appears in the following Collection(s)

Show simple item record