Contractive maps on normed linear spaces and their applications to nonlinear matrix equations

Linear Algebra and Its Applications

Volumn 418, Issue 1, 2006, Pages 292-311

  Reurings, Martine C B ^a  

^a SWOV INSTITUTE FOR ROAD SAFETY RESEARCH   (Netherlands)

Author keywords

Contractions on cones; Fixed point theorem; Nonlinear matrix equations

Indexed keywords

CONFORMAL MAPPING; MATRIX ALGEBRA; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

CONTRACTIONS ON CONES; FIXED POINT THEOREM; NONLINEAR MATRIX EQUATIONS;

NONLINEAR EQUATIONS;

EID: 33748202971     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2006.02.005     Document Type: Article

References (29)

1. Ambrosetti A., and Prodi G. A Primer of Nonlinear Analysis. Cambridge Studies in Advanced Mathematics vol. 34 (1995), Cambridge University Press
2. *. Linear Algebra Appl. 134 (1990) 53-62
3. Bhatia R. First and second order perturbation bounds for the operator absolute value. Linear Algebra Appl. 208/209 (1994) 367-376
4. Bhatia R. Matrix Analysis. Graduate Texts in Mathematics vol. 169 (1997), Springer-Verlag
5. Bhatia R., Singh D., and Sinha K.B. Differentation of operator functions and perturbation bounds. Commun. Math. Phys. 191 (1998) 603-611
6. Bhatia R., and Sinha K.B. Variation of real powers of positive operators. Indiana Univ. Math. J. 43 (1994) 913-925
7. -2A = I. Linear Algebra Appl. 394 (2005) 39-51
8. -nA = Q. Comput. Math. Appl. 41 (2001) 579-588
9. El-Sayed S.M. On the positive definite solutions for a nonlinear matrix equation. Int. Math. J. 4 (2003) 27-42
10. -1A = I. Int. J. Comput. Math. 80 (2003) 1527-1534
11. -αA = I. Linear Algebra Appl. 403 (2005) 45-52
12. El-Sayed S.M., and Ran A.C.M. On an iteration method for solving a class of nonlinear matrix equations. SIAM J. Matrix Anal. Appl. 28 (2001) 632-645
13. -1A = Q. Linear Algebra Appl. 186 (1993) 255-275
14. -qA = Q. Linear Algebra Appl. 404 (2005) 166-182
15. -δA = Q. Linear Algebra Appl. 412 (2006) 154-160
16. -nA = I, Lecture Notes in Computer Science, Numerical Analysis and its Applications 2000, 2001, pp. 377-384.
17. -nA = Q. Appl. Math. Comput. 156 (2004) 513-525
18. -nA = I. Appl. Math. Comput. 168 (2005) 1340-1356
19. -1A = Q. Linear Algebra Appl. 379 (2004) 113-135
20. -nA = Q. Linear Algebra Appl. 395 (2005) 313-331
21. -2A = I. Linear Algebra Appl. 297 (1998) 303-316
22. -2A = I. Linear Algebra Appl. 326 (2001) 27-44
23. -1A = I iteratively. Math. Comput. 74 (2005) 263-278
24. Konstantinov M., Mehrmann V., Petkov P., and Gu D. Perturbation Theory for General Matrix Equations (2005), Softtrade, Sofia
25. -2A = I. Appl. Math. Comput. 164 (2005) 189-200
26. * F (X) A = Q: solutions and perturbation theory. Linear Algebra Appl. 346 (2002) 15-26
27. M.C.B. Reurings, Symmetric matrix equations, Ph.D. thesis, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands, 2003. Available from: .
28. -1A = P. II. Linear Algebra Appl. 362 (2003) 211-228
29. -2A = I. Linear Algebra Appl. 372 (2003) 295-304