Curtain, Ruth - ed. ; Kaashoek, Rien - ed.
Infinite-Dimensional Systems Theory and Operator Theory
It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial G([lambda]) (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. ; In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of G([lambda]). The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.
Zielona Góra: Uniwersytet Zielonogórski
AMCS, volume 11, number 6 (2001) ; kliknij tutaj, żeby przejść
Biblioteka Uniwersytetu Zielonogórskiego
2021-09-03
2021-07-22
57
https://zbc.uz.zgora.pl/repozytorium/publication/65600
Nazwa wydania | Data |
---|---|
Matrix quadratic equations, column/row reduced factorizations and an inertia theorem for matrix polynomials | 2021-09-03 |
Walicka, Anna Jurczak, Paweł Falicki, Jarosław Jurczak, Paweł - red.
Walicka, Anna Jurczak, Paweł Jurczak, Paweł - red.
Pandolfi, Luciano Curtain, Ruth - ed. Kaashoek, Rien - ed.
Bilski, Jarosław Korbicz, Józef - red. Uciński, Dariusz - red.
Bylina, Beata Bylina, Jarosław Korbicz, Józef - ed.
Walicka, Anna Walicki, Edward Jurczak, Paweł Jurczak, Paweł - red.
Walicka, Anna Falicki, Jarosław Jurczak, Paweł - red.
Das, Utpal Jyoti Begum, Jubi Jurczak, Paweł - red.