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Detalji o izabranom predavanju:
| Seminar: | Seminar za numeričku matematiku i znan. računanje |
| Naziv predavanja: | The Newton polygon and structured eigenvalue perturbation |
| Predavač: | Julio Moro, Departamento de Matemáticas, Universi |
| Vrijeme: |
08.02.2016 12:15 |
| Predavaonica: | 104 |
| Tip: |
Gost seminara |
| Opis: | The Newton polygon, an elementary geometric construction first devised by Sir Isaac Newton, has been often used in the context of perturbation theory as a tool for deriving explicit first-order eigenvalue perturbation expansions. On one hand, this usually gives useful information on the directions in which perturbed eigenvalues move, something which is crucial in several practical situations when eigenvalues need to be pushed in certain specific directions, or must be moved as fast as possible away from a critical (or dangerous) region by a small perturbation. On the other hand, these asymptotic expansions often lead to sharp bounds on the condition number of eigenvalues.
Most of these results, however, are obtained for arbitrary,
nonstructured perturbations. If the matrix or operator under study belongs to a specific class of structured operators, it makes sense to consider only perturbations having the same structure, thereby restricting the admissible Newton polygons. So far, it seems that the structures most amenable to such a structured perturbation analysis via the Newton polygon are those defined via indefinite scalar products for which structured canonical forms are available.
In this talk we will both review classic results for unstructured perturbation as well as explore the case of structured perturbations. Taking as a guide a specific example, involving zero eigenvalues of complex skew-symmetric matrices, we will illustrate the interplay between matrix structure and the Newton polygon. |
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