How Near is a Stable Matrix to an Unstable Matrix?
| dc.contributor.author | Van Loan, Charles | en_US |
| dc.date.accessioned | 2007-04-23T16:54:02Z | |
| dc.date.available | 2007-04-23T16:54:02Z | |
| dc.date.issued | 1984-10 | en_US |
| dc.description.abstract | In this paper we explore how close a given stable matrix A is to being unstable. As a measure of "how stable" a stable matrix is, the spectral abscissa is shown to be flawed. A better measure of stability is the Frobenius norm of the smallest perturbation that shifts one of A's eigenvalues to the imaginary axis. This leads to a singular value minimization problem that can be approximately solved by heuristic means. However, the minimum destabilizing perturbation may be complex even when A is real. This suggests that in the real case we look for the smallest real perturbation that shifts one of the eigenvalues to the imaginary axis. Unfortunately, a difficult constrained minimization problem ensues and no practical estimation technique could be devised. | en_US |
| dc.format.extent | 1247022 bytes | |
| dc.format.extent | 330014 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.format.mimetype | application/postscript | |
| dc.identifier.citation | http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR84-649 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1813/6488 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Cornell University | en_US |
| dc.subject | computer science | en_US |
| dc.subject | technical report | en_US |
| dc.title | How Near is a Stable Matrix to an Unstable Matrix? | en_US |
| dc.type | technical report | en_US |