Solutions and perturbation analysis for the nonlinear matrix equation X + ∑i=1m Ai* X -1Ai = i

Applied Mathematics and Computation

Volumn 218, Issue 8, 2011, Pages 4458-4466

  Duan, Xuefeng ^a,b   Li, Chunmei ^a   Liao, Anping ^c  

^a SHANGHAI UNIVERSITY   (China)

^b GUILIN UNIVERSITY OF ELECTRONIC TECHNOLOGY   (China)

^c HUNAN UNIVERSITY   (China)

Author keywords

Necessary condition; Nonlinear matrix equation; Perturbation bound; Positive definite solution; Sufficient condition

Indexed keywords

NECESSARY CONDITION; NONLINEAR MATRIX EQUATION; PERTURBATION BOUND; POSITIVE DEFINITE SOLUTION; SUFFICIENT CONDITIONS;

DIFFERENTIATION (CALCULUS); NONLINEAR EQUATIONS;

MATRIX ALGEBRA;

EID: 81855201802     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.10.026     Document Type: Article

References (27)

1. Z.Z. Bai, X.X. Guo, and J.F. Yin On two iteration methods for the quadratic matrix equation Inter. J. Numer. Anal. Mod. 2 2005 114 122
2. -tA = Q Appl. Math. Comput. 217 2010 2448 2456
3. -tA = Q Linear Algebra Appl. 429 2008 673 687
4. δiAi = Q, Linear Algebra Appl. 429 2008 110 121
5. -qA = Q(q ≥ 1) Math. Comput. Mod. 49 2009 936 945
6. -1A = Q Linear Algebra Appl. 186 1993 255 275
7. -1A = I Linear Algebra Appl. 194 1993 91 108
8. S.M. El-Sayed, and A.C.M. Ran On an iterative method for solving a class of nonlinear matrix equations SIAM J. Matrix Anal. Appl. 23 2001 632 645
9. B.R. Fang, J.D. Zhou, and Y.M. Li Matrix Theory 2006 Tsinghua University Press Beijing
10. -1A = I Linear Algebra Appl. 429 2008 2098 2112
11. C.H. Guo, and P. Lancaster Iterative solution of two matrix equations Math. Comput. 68 1999 1589 1603
12. 1Ai = I, Appl. Math. Comput. 216 2010 3480 3485
13. -1A = Q Linear Algebra Appl. 413 2006 81 92 (Pubitemid 43003867)
14. -1A = I iteratively Math. Comput. 74 2004 263 278 (Pubitemid 40058244)
15. -nA = Q J. Comput. Appl. Math. 193 2006 277 301 (Pubitemid 44287920)
16. 1A 2 = I, Bull. Braz. Math. Soc. 222 2008 645 654
17. J.H. Long, X.Y. Hu, and L. Zhang Improved Newton method with exact linear searches to solve quadratic matrix equation J. Comput. Appl. Math. 39 2008 371 386
18. n Linear Algebra Appl. 368 2003 83 97
19. M. Monsalve, and M. Raydan A new inversion-free method for a rational matrix equation Linear Algebra Appl. 433 2010 64 71
20. -1A = Q Math. Comput. 71 2001 1189 1204
21. -αA = Q J. Comput. Appl. Math. 200 2007 520 527 (Pubitemid 46084884)
22. S.G. Wang, M.X. Wu, and Z.Z. Jia Matrix Inequalities 2006 Science Press Beijing
23. -1A = P Linear Algebra Appl. 336 2001 61 70
24. J.G. Sun Perturbation bounds for the Cholesky and QR factorizations BIT 31 1991 341 352
25. -tA = Q Linear Algebra Appl. 431 2009 1409 1421
26. X.Z. Zhan Computing the extreme positive definite solutions of a matrix equation SIAM J. Sci. Comput. 17 1996 632 645
27. -1A = I Linear Algebra Appl. 247 1996 337 345