Abstract
The purpose of this paper is to propose a definition of a set of singular values and a singular value decomposition associated with a linear operator defined on arbitrary normed linear spaces. This generalizes the usual notion of singular values and singular value decompositions to operators defined on spaces equipped with the p-norm, where p is arbitrary. Basic properties of these generalized singular values are derived and the problem of optimal rank approximation of linear operators is investigated in this context. We give sufficient conditions for the existence of optimal rank approximants in the p-induced norm and discuss an application of generalized singular values for the identification of dynamical systems from data.
| Original language | Undefined |
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| Pages | 15651 |
| Number of pages | 11 |
| Publication status | Published - Aug 2002 |
| Event | 15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002 - University of Notre Dame, Notre Dame, United States Duration: 12 Aug 2002 → 16 Aug 2002 Conference number: 15 |
Conference
| Conference | 15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002 |
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| Abbreviated title | MTNS 2002 |
| Country/Territory | United States |
| City | Notre Dame |
| Period | 12/08/02 → 16/08/02 |
| Other | 12-16 Aug 2002 |
Keywords
- Linear systems
- EWI-16648
- Singular values
- Optimalidentification
- Rank reduction
- Optimal approximation
- IR-69043