On the Powers of a Matrix with Perturbations
| dc.contributor.author | Stewart, G. W. | en_US |
| dc.date.accessioned | 2004-05-31T23:15:12Z | |
| dc.date.available | 2004-05-31T23:15:12Z | |
| dc.date.created | 2001-12 | en_US |
| dc.date.issued | 2002-01-31 | en_US |
| dc.description.abstract | Let $A$ be a matrix of order $n$. The properties of the powers $A^{k}$ of $A$ have been extensively studied in the literature. This paper concerns the perturbed powers \[ P_{k} = (A+E_{k})(A+E_{k-1})\cdots(A+E_{1}), \] where the $E_{k}$ are perturbation matrices. We will treat three problems concerning the asymptotic behavior of the perturbed powers. First, determine conditions under which $P_{k}\rightarrow 0$. Second, determine the limiting structure of $P_{k}$. Third, investigate the convergence of the power method with error: that is, given $u_{1}$, determine the behavior of $u_{k} = \nu_{k}P_{k}u_{1}$, where $\nu_{k}$ is a suitable scaling factor. (Also UMIACS-TR-2001-91) | en_US |
| dc.format.extent | 155585 bytes | |
| dc.format.mimetype | application/postscript | |
| dc.identifier.uri | http://hdl.handle.net/1903/1172 | |
| dc.language.iso | 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 |
| dc.relation.ispartofseries | UM Computer Science Department; CS-TR-4317 | en_US |
| dc.relation.ispartofseries | UMIACS; UMIACS-TR-2001-91 | en_US |
| dc.title | On the Powers of a Matrix with Perturbations | en_US |
| dc.type | Technical Report | en_US |