Analysis of the Residual Arnoldi Method
| dc.contributor.author | Lee, Che-Rung | |
| dc.contributor.author | Stewart, G. W. | |
| dc.date.accessioned | 2007-10-15T17:23:08Z | |
| dc.date.available | 2007-10-15T17:23:08Z | |
| dc.date.issued | 2007-10-15 | |
| dc.description.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's method. In this paper we give a mathematical analysis of these new methods. | en |
| dc.format.extent | 318799 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/7428 | |
| dc.language.iso | en_US | en |
| dc.relation.ispartofseries | UM Computer Science Department | en |
| dc.relation.ispartofseries | CS-TR-4890 | en |
| dc.relation.ispartofseries | UMIACS | en |
| dc.relation.ispartofseries | UMIACS-TR-2007-45 | en |
| dc.title | Analysis of the Residual Arnoldi Method | en |
| dc.type | Technical Report | en |