Autor:
Karelin, Irina ; Lerer, Leonid
Współtwórca:
Curtain, Ruth - ed. ; Kaashoek, Rien - ed.
Tytuł:
Podtytuł:
Infinite-Dimensional Systems Theory and Operator Theory
Tytuł publikacji grupowej:
Temat i słowa kluczowe:
matrix quadratic equations ; Bezoutians ; inertia ; column (row) reduced polynomials ; factorization ; algebraic Riccati equation ; extremal solutions
Abstract:
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.
Wydawca:
Zielona Góra: Uniwersytet Zielonogórski
Data wydania:
Typ zasobu:
Strony:
Źródło:
AMCS, volume 11, number 6 (2001) ; kliknij tutaj, żeby przejść