Perturbation analysis of the Hermitian positive definite solution of the matrix equation X - A* X-2 A = I

Linear Algebra and Its Applications

Volumn 394, Issue 1-3, 2005, Pages 39-51

  Cheng, Mingsong ^a   Xu, Shufang ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Condition number; Nonlinear matrix equation; Perturbation bound

Indexed keywords

LARGE SCALE SYSTEMS; NONLINEAR EQUATIONS; NUMBER THEORY; PERTURBATION TECHNIQUES; SENSITIVITY ANALYSIS; THEORY;

CONDITION NUMBER; FIXED-POINT THEORY; NONLINEAR MATRIX EQUATION; PERTURBATION BOUND;

MATRIX ALGEBRA;

EID: 7544221399     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2004.05.013     Document Type: Article

References (10)

1. -n A = Q, Comput. Math. Appl. 41 (2001) 579-588.
2. S.M. El-Sayed, A.C.M. Ran, On an iteration method for solving a class of nonlinear matrix equations, SIAM J. Matrix Anal. Appl. 23 (2001) 632-645.
3. A. Graham, Kronecker Products and Matrix Calculus: with Applications, Ellis Horwood Limited, Chichester, 1981.
4. -n A = I, Numerical Analysis and its Applications, Lecture Notes in Comput. Sci. 2000 (2001) 377-384.
5. -2 A = I, Linear Algebra Appl. 326 (2001) 27-44.
6. n, Linear Algebra Appl. 368 (2003) 83-97.
7. A.C.M. Ran, M.C.B. Reurings, On the nonlinear matrix equation X + A*F(X)A = Q: solutions and perturbation theory, Linear Algebra Appl. 346 (2002) 15-26.
8. M.C.B. Reurings, Symmetric Matrix Equations, Ph.D. Thesis, Vrije Universiteit, Amsterdam, 2003 (ISBN 90-9016681-5).
9. J.R. Rice, A theory of condition, J. SIAM Numer. Anal. 3 (1966) 287-310.
10. -1 A = P. II, Linear Algebra Appl. 362 (1966) 211-228.