The symmetric linear matrix equation

Electronic Journal of Linear Algebra

Volumn 9, Issue , 2002, Pages 93-107

  Ran, André M ^a   Reurings, Martine C B ^a  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Linear matrix equation; Positive definite solutions; Uniqueness of solutions

Indexed keywords

EID: 0042566426     PISSN: 10813810     EISSN: None     Source Type: Journal    
DOI: 10.13001/1081-3810.1075     Document Type: Article

References (11)

1. S.M. El-Sayed and A.C.M. Ran. On an iteration method for solving a class of nonlinear matrix equations. SIAM J. Matrix Anal. Appl., 28:632-645, 2001.
2. I. Gohberg and S. Goldberg. Basic Operator Theory. Birkḧauser, Boston, 1980.
3. W. Greenberg, C. van der Mee, and V. Protopopescu. Boundary value problems in abstract kinetic theory, Volume 23 of Operator Theory: Advances and Applications. Birkḧauser, Basel, 1987.
4. M.A. Krasnosel'skii. Positive Solutions of Operator Equation. P. Noordho., Groningen, 1964.
5. P. Lancaster. Explicit solution of linear matrix equations. SIAM Rev., 12:544-566, 1970.
6. P. Lancaster and L. Rodman. Algebraic Riccati Equations. Oxford University Press, New York, 1995.
7. P. Lancaster and M. Tismenetsky. The Theory of Matrices. Academic Press, 1985.
8. A.C.M. Ran and M.C.B. Reurings. On the nonlinear matrix equation X + A*F(X)A = Q: Solutions and perturbation theory. Linear Algebra Appl., 346:15-26, 2002.
9. P. Roózsa. Lineare matrizengleichungen und kroneckersche produkte. Z. Angew. Math. Mech., 58T:395-397, 1978.
10. L.A. Sakhnovich. Interpolation Theory and Its Applications, Volume 428 of Mathematics and Its Applications. Kluwer Academic Publishers, Dordrecht, 1997.
11. W.J. Vetter. Vector structures, solutions of linear matrix equations. Linear Algebra Appl., 10:181-188, 1975.