Linearization, sensitivity and backward perturbation analysis of multiparameter eigenvalue problems
| dc.contributor.author | Ghosh, Arnab | |
| dc.date.accessioned | 2019-07-08T11:34:19Z | |
| dc.date.accessioned | 2023-10-26T09:43:02Z | |
| dc.date.available | 2019-07-08T11:34:19Z | |
| dc.date.available | 2023-10-26T09:43:02Z | |
| dc.date.issued | 2017 | |
| dc.description | Supervisor: Rafikul Alam | en_US |
| dc.description.abstract | We develop a general framework for the sensitivity and backward perturbation analysis of linear and polynomial MEPs. For a general norm on the space of MEPs, we define the condition number cond( ,W) of a simple eigenvalue of an MEPWand derive three equivalent representations of cond( ,W).We also analyze holomorphic perturbation of a simple eigenvalue of W. Further, we define the backward error ( ,W) of an approximate eigenvalue of W. We determine ( ,W) and construct an optimal perturbation W such that 2 (W+ W) and ||| W||| = ( ,W). We also define the backward error ( , x,W) of an approximate eigenpair ( , x := x1 · · · xm) 2 Cm × (Cn1 · · · Cnm). We determine ( , x,W) and construct an optimal perturbation W such that W( )x + W( )x = 0 and ||| W||| = ( , x,W). We define and analyze two vector spaces, namely, the right ansatz space and the left ansatz space of potential linearizations of a two-parameter matrix polynomial of the form P( , μ) := Pk i=0 Pk−i j=0 iμjAij . We also analyze conditions under which a pencil in the ansatz spaces is a linearization of P( , μ). We consider structured linear MEPs and define structured backward error S( , x,W) of an approximate eigenpair ( , x := x1 · · · xm). We determine S( , x,W) and construct an optimal structured perturbation W such that W( )x + W( )x = 0 and ||| W||| = S( , x,W). | en_US |
| dc.identifier.other | ROLL NO.09612307 | |
| dc.identifier.uri | https://gyan.iitg.ac.in/handle/123456789/1091 | |
| dc.language.iso | en | en_US |
| dc.relation.ispartofseries | TH-1902; | |
| dc.subject | MATHEMATICS | en_US |
| dc.title | Linearization, sensitivity and backward perturbation analysis of multiparameter eigenvalue problems | en_US |
| dc.type | Thesis | en_US |
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