Structured perturbations of Drazin inverse

Applied Mathematics and Computation

Volumn 158, Issue 2, 2004, Pages 419-432

  Diao, Huaian ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Drazin inverse; Singular linear system with index k; Structured perturbations

Indexed keywords

DIFFERENCE EQUATIONS; INVERSE PROBLEMS; ITERATIVE METHODS; MARKOV PROCESSES; MATHEMATICAL MODELS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; SET THEORY;

DRAZIN INVERSE; SINGULAR LINEAR SYSTEM WITH INDEX K; STRUCTURED PERTURBATIONS;

LINEAR SYSTEMS;

EID: 4744365706     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.08.099     Document Type: Article

References (28)

1. Ben-Israel A., Greville T.N.E. Generalized Inverses: Theory and Applications. second ed. 2003;Springer-Verlag, New York.
2. Campbell S.L., Meyer C.D. Generalized Inverse of Linear Transformations. 1979;Pitman.
3. Castro González N., Koliha J.J., Wei Y. On integral representation of the Drazin inverse in Banach space. Proc. Edinburgh Math. Soc. 45:2002;327-331.
4. Castro González N., Koliha J.J., Wei Y. Error bounds for perturbation of the Drazin inverse of closed operators with equal spectral projections. Appl. Anal. 81:2002;915-928.
5. H. Diao, Y. Wei, Structured perturbation of group inverse and singular linear system with index one, submitted.
6. H. Diao, Y. Wei, S. Qiao, Displacement rank of the Drazin inverse, Technical Report CAS 03-01-SQ, McMaster University, to appear in J. Comput. Appl. Math., 2003.
7. Djordjević D.S., Wei Y. Additive results for the generalized Drazin inverse. J. Austral. Math. Soc. 73:2002;115-125.
8. Eiermann M., Marek I., Niethammer W. On the solution of singular linear systems of algebraic equations by semiiterative methods. Numer. Math. 53:1988;265-283.
9. Freund R.W., Hochbruck M. On the use of two QMR algorithms for solving singular systems and applications in Markov chains modelling. Numer. Linear Algebra Appl. 1:1994;403-420.
10. Kirkland S.J., Neumann M., Shader B.L. Application of Paz'z inequality to perturbation bounds for Markov chains. Linear Algebra Appl. 268:1998;183-196.
11. Rakočević V., Wei Y. The perturbation theory for the Drazin inverse and its applications II. J. Austral. Math. Soc. 70:2001;189-197.
12. Rump S.M. Structured perturbations Part I: Normwise distances. SIAM J. Matrix Anal. Appl. 25:2003;1-30.
13. Rump S.M. Structured perturbation Part II: Componentwise distances. SIAM J. Matrix Anal. Appl. 25:2003;31-56.
14. Wei Y. A characterization and representation of the Drazin inverse. SIAM J. Matrix Anal. Appl. 17:1996;744-747.
15. Wei Y., Wang G. The perturbation theory for the Drazin inverse and its applications. Linear Algebra Appl. 258:1997;179-186.
16. Wei Y. Index splitting for the Drazin inverse and the singular linear system. Appl. Math. Comput. 95:1998;115-124.
17. Wei Y., Wu H. Convergence properties of Krylov subspace methods for singular linear system with arbitrary index. J. Comput. Appl. Math. 104:2000;305-318.
18. Wei Y. Representation and perturbation of the Drazin inverse in Banach space. J. Contemp. Math. 21:2000;39-46.
19. Wei Y., Wu H. The perturbation of Drazin inverse and oblique projection. Appl. Math. Lett. 13:2000;77-83.
20. Wei Y. Successive matrix squaring algorithm for computing the Drazin inverse. Appl. Math. Comput. 108:2000;67-75.
21. Wei Y., Wu H. Additional results on index splittings for Drazin inverse solution of singular linear systems. Electron. J. Linear Algebra. 8:2001;83-93.
22. Wei Y., Wu H. Challenging problems on the perturbation of Drazin inverse. Annal. Oper. Res. 103:2001;371-378.
23. Wei Y., Wu H. On the use of incomplete semiiterative methods for singular linear systems and applications in Markov chain modelling. Appl. Math. Comput. 125:2002;245-259.
24. Wei Y. Perturbation bound of Drazin inverse. Appl. Math. Comput. 125:2002;231-244.
25. Wei Y. The Drazin inverse of a modified matrix. Appl. Math. Comput. 125:2002;295-301.
26. Wei Y., Qiao S. The representation and approximation for the Drazin inverse in Hilbert space. Appl. Math. Comput. 138:2003;77-89.
27. Wei Y., Wang G., Wang D. Condition number of Drazin inverse and their condition numbers of singular systems. Appl. Math. Comput. 146:2003;455-467.
28. W. Xu, Y. Wei, S. Qiao, Condition numbers for structured least squares, Technical Report CAS 03-04-SQ, McMaster University, 2003.