On the nonlinear matrix equation X - ∑i = 1m Ai* Xδi Ai = Q

Linear Algebra and Its Applications

Volumn 429, Issue 1, 2008, Pages 110-121

  Duan, Xuefeng ^a   Liao, Anping ^a   Tang, Bin ^a  

^a HUNAN UNIVERSITY   (China)

Author keywords

Iterative method; Nonlinear matrix equation; Positive definite solution

Indexed keywords

ITERATIVE METHODS; MATRIX ALGEBRA; NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING;

NONLINEAR MATRIX EQUATION; POSITIVE DEFINITE SOLUTION;

NONLINEAR EQUATIONS;

EID: 42749085747     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.02.014     Document Type: Article

References (18)

1. - 2 A = I. Linear Algebra Appl. 394 (2005) 39-51
2. El-Sayed S.M., and Ran A.C.M. On an iterative method for solving a class of nonlinear matrix equations. SIAM J. Matrix Anal. Appl. 23 (2001) 632-645
3. - 1 N. Linear Algebra Appl. 247 (1996) 359-373
4. Guo D. Existence and uniqueness of positive fixed point for mixed monotone operators with applications. Appl. Anal. 46 (1992) 91-100
5. Guo D., and Lakshmikantham V. Nonlinear problems in abstract cones, Notes and reports in mathematices. Science and Engineering vol. 5 (1988), Academic Press, Inc.
6. Guo C.H., and Lancaster P. Iterative solution of two matrix equations. Math. Comput. 68 (1999) 1589-1603
7. Guo D. Nonlinear Functional Analysis (2001), Shandong Sci. and Tech. Press, Jinan (in Chinese)
8. q A = Q (q > 0). Math. Numer. Sinica 29 (2007) 73-80 in Chinese
9. V.I. Hasanov, Solutions and perturbation theory of nonlinear matrix equations, PhD Thesis, Sofia, 2003.
10. - q A = Q. Linear Algebra Appl. 404 (2005) 166-182
11. - 1 A = I iteratively. Math. Comput. 74 (2004) 263-278
12. - n A = Q. J. Comput. Appl. Math. 193 (2006) 277-301
13. n. Linear Algebra Appl. 368 (2003) 83-97
14. - n A = I. Numer. Math. - A J. Chin. Univ. 26 (2004) 156-161
15. M.C.B. Reurings, Symmetric matrix equation, PhD Thesis, Vrije Universiteit, Amsterdan, 2003, ISBN 90-9016681-5.
16. Ran A.C.M., and Reurings M.C.B. A nonlinear matrix equation connected to interpolation theory. Linear Algebra Appl. 379 (2004) 289-302
17. Shi X.Q., Liu F.S., Umoh H., and Gibson F. Two kinds of nonlinear matrix equations and their corresponding matrix sequences. Linear Multilinear Algebra 52 (2004) 1-15
18. Zhan X. Matrix Inequalities (2002), Springer-Verlag, Berlin