Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials
International Journal of Applied Mathematics and Computer Science (2001)
- Volume: 11, Issue: 6, page 1285-1310
- ISSN: 1641-876X
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topKarelin, Irina, and Lerer, Leonid. "Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials." International Journal of Applied Mathematics and Computer Science 11.6 (2001): 1285-1310. <http://eudml.org/doc/207556>.
@article{Karelin2001,
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 (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 . 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.},
author = {Karelin, Irina, Lerer, Leonid},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {column (row) reduced polynomials; extremal solutions; inertia; matrix quadratic equations; algebraic Riccati equation; factorization; Bezoutians; Bézoutians; controllability; observability},
language = {eng},
number = {6},
pages = {1285-1310},
title = {Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials},
url = {http://eudml.org/doc/207556},
volume = {11},
year = {2001},
}
TY - JOUR
AU - Karelin, Irina
AU - Lerer, Leonid
TI - Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 6
SP - 1285
EP - 1310
AB - 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 (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 . 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.
LA - eng
KW - column (row) reduced polynomials; extremal solutions; inertia; matrix quadratic equations; algebraic Riccati equation; factorization; Bezoutians; Bézoutians; controllability; observability
UR - http://eudml.org/doc/207556
ER -
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