Autor:

Karelin, Irina ; Lerer, Leonid

Współtwórca:

Curtain, Ruth - ed. ; Kaashoek, Rien - ed.

Tytuł:

Matrix quadratic equations, column/row reduced factorizations and an inertia theorem for matrix polynomials

Podtytuł:

Infinite-Dimensional Systems Theory and Operator Theory

Tytuł publikacji grupowej:

AMCS, volume 11 (2001)

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:

2001

Typ zasobu:

artykuł

Strony:

1285-1310

Źródło:

AMCS, volume 11, number 6 (2001) ; kliknij tutaj, żeby przejść

Jezyk:

eng

Licencja CC BY 4.0:

kliknij tutaj, żeby przejść

Prawa do dysponowania publikacją:

Biblioteka Uniwersytetu Zielonogórskiego