TY - GEN
A1 - Karelin, Irina
A1 - Lerer, Leonid
A2 - Curtain, Ruth - ed.
A2 - Kaashoek, Rien - ed.
PB - Zielona Góra: Uniwersytet Zielonogórski
N2 - 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.
N2 - 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.
L1 - http://zbc.uz.zgora.pl/Content/58814/AMCS_2001_11_6_5.pdf
L2 - http://zbc.uz.zgora.pl/Content/58814
KW - matrix quadratic equations
KW - Bezoutians
KW - inertia
KW - column (row) reduced polynomials
KW - factorization
KW - algebraic Riccati equation
KW - extremal solutions
T1 - Matrix quadratic equations, column/row reduced factorizations and an inertia theorem for matrix polynomials
UR - http://zbc.uz.zgora.pl/dlibra/docmetadata?id=58814
ER -