Iterative methods for the extremal positive definite solution of the matrix equation X + A* X- α A = Q

Journal of Computational and Applied Mathematics

Volumn 200, Issue 2, 2007, Pages 520-527

  Peng, Zhen yun ^a   El Sayed, Salah M ^b   Zhang, Xiang lin ^a  

^a HUNAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b BENHA UNIVERSITY   (Egypt)

Author keywords

Iterative method; Matrix equation; Positive definite matrix; The maximal solution; The minimal solution.

Indexed keywords

ALGORITHMS; ITERATIVE METHODS; NONLINEAR EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

MATRIX EQUATIONS; MAXIMAL SOLUTION; MINIMAL SOLUTION; POSITIVE DEFINITE MATRIX;

MATRIX ALGEBRA;

EID: 33846178670     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.01.033     Document Type: Article

References (23)

1. *. Linear Algebra Appl. 134 (1990) 53-62
2. Bhatia R. Matrix analysis, Graduate Texts in Mathematics (1997), Spring, Berlin
3. S.M. El-Sayed, Investigation of the special matrices and numerical methods for the special matrix equation, Ph.D. Thesis, Sofia, 1996 (in Bulgarian).
4. El-Sayed S.M. Two sided iteration methods for computing positive definite solutions of a nonlinear matrix equation. J. Austral. Math, Soc. Ser. B. 44 (2003) 1-8
5. El-Sayed S.M., and Al-Dbiban A.M. On positive definite solutions of nonlinear matrix equation. Appl. Math. Comput. 151 (2004) 533-541
6. - 1 A = Q. J. Comput. Appl. Math. 181 (2005) 148-156
7. -2m A = I. Appl. Math. Comput. 128 (2002) 99-108
8. - α A = I. Linear Algebra Appl. 403 (2005) 45-52
9. El-Sayed S.M., and Ran A.C.M. On an iteration methods for solving a class of nonlinear matrix equations. SIAM. J. Matrix Anal. Appl. 23 (2001) 632-645
10. - 1 A = I. Linear Algebra Appl. 194 (1993) 91-108
11. *. Linear Algebra Appl. 247 (1996) 359-373
12. Furuta T. Operator inequalities associated with Holder-Mccarthy and kantorovich inequalities. J. Inequal. Appl. 6 (1998) 137-148
13. Guo C.H., and Lancaster P. Iterative solution of two matrix equations. Math. Comput. 228 (1999) 1589-1603
14. V.I. Hasanov, Positive definite solutions of a nonlinear matrix equation, in: mathematics and education in mathematics, Proceedings of Twenty Eighth Spring Conference of the Union of Bulgarian Mathematics, 1999, pp. 107-112.
15. V.I. Hasanov, Solutions and perturbation theory of the nonlinear matrix equations, Ph.D. Thesis, Sofia, 2003 (in Bulgarian).
16. - q A = Q. Linear Algebra Appl. 404 (2005) 166-182
17. - n A = Q. Appl. Math. Comput. 156 (2004) 513-525
18. - 2 A = I. Linear Algebra Appl. 279 (1998) 303-316
19. - 2 A = I. Linear Algebra Appl. 326 (2001) 27-44
20. Lancaster P., and Rodman L. Algebraic Riccati Equations (1995), Oxford Science Publishers, Oxford
21. M. Parodi, La localisation des valeurs caracterisiques des matrices etses applications, Gauthiervillars, Paris, 1959.
22. m) A = I. Appl. Math. Comput. 173 (2006) 992-1013
23. Zhan X. Computing the extremal positive definite solutions of a matrix equation. SIAM J. Sci. Comput. 17 (1996) 1167-1174