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Detalji o izabranom predavanju:
| Seminar: | Seminar za numeričku matematiku i znan. računanje |
| Naziv predavanja: | Inverse Problems for Structured Matrix Polynomials |
| Predavač: | Vasilije Perović, University of Rhode Island, SAD |
| Vrijeme: |
06.06.2024 12:15 |
| Predavaonica: | 201 |
| Tip: |
Gost seminara |
| Opis: | Matrix polynomials arise in a variety of application areas, including the vibration analysis of mechanical structures, optimal control, and linear systems theory. The key structural data of a matrix polynomial in many such applications are its degree, its eigenvalues and elementary divisors (both finite and infinite), together with its left and right minimal indices. A fundamental inverse problem for matrix polynomials, then, consists of two aspects:
- characterizing the lists of structural data, L, that can be realized by some matrix polynomial of the given degree, and
- for each such realizable list of structural data, constructing a realization in such a way that the given structural data is transparently visible.
In this talk, we provide a characterization of those structural lists L that are realizable by two special families of matrix polynomials, namely the quadratic T-palindromic and T-alternating matrix polynomials over an algebraically closed field. We also describe how to concretely construct a realization for any admissible L, that at the same time allows one to easily read off the original structural data in L. As time permits, we will discuss the modifications needed to solve this inverse problem when the underlying field is the real numbers. |
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