Effect of linear perturbation on spectra of matrices

Linear Algebra and Its Applications

Volumn 368, Issue , 2003, Pages 329-342

  Alam, R ^a   Bora, S ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

Author keywords

Spectrum; Dissociation; Isospectral; Spectral variety; Stable and unstable eigenvalues

Indexed keywords

EID: 0038392505     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(02)00692-4     Document Type: Article

References (19)

1. R. Alam, and S. Bora Stability of eigenvalues and spectral decompositions under linear perturbation Linear Algebra Appl. 364 2003 199 221
2. M. Artin Algebra 1994 Prentice-Hall of India Private Limited New Delhi
3. B. Aupetit A Primer on Spectral Theory 1991 Springer-Verlag New York
4. H. Baumgartel Analytic Perturbation Theory for Matrices and Operators 1985 Birkhauser
5. S. Bora, A Geometric Analysis of Spectral Stability of Matrices and Operators, PhD thesis, IIT Guwahati, 2001
6. J.V. Burke, and M.L. Overton Stable perturbation of nonsymmetric matrices Linear Algebra Appl. 171 1992 249 273
7. F. Chatelin Spectral Approximation of Linear Operators 1983 Academic Press New York
8. F. Chaitin-Chatelin, V. Tomazou, and E. Traviesas Accuracy assessment for eigencomputations: variety of backward errors and pseudospectra Linear Algebra and Appl. 309 2000 73 83
9. D. Cox, J. Little, and D. O'Shea Ideals, Varieties, and Algorithms 1997 Springer-Verlag New York
10. T. Kato Perturbation Theory for Linear Operators 1976 Springer New York
11. V.B. Lidskii Perturbation theory of non-conjugate operators USSR Comp. Math. Math. Phys. 6 1966 73 85
12. R.A. Lippert, and A. Edelman The computation and sensitivity of double eigenvalues Z. Chen, Y. Li, C.A. Micchelli, Y. Xu, Advances in Computational Mathematics: Proc. Gaungzhou International Symposium 1999 Dekker New York 353 393
13. Y. Ma, and A. Edelman Non-generic eigenvalue perturbations of Jordan blocks Linear Algebra Appl. 273 1998 45 63
14. J. Moro, J.V. Burke, and M.L. Overton On the Lidskii-Vishik-Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure SIAM J. Matrix Anal. Appl. 18 4 1997 793 817
15. V. Simoncini Remarks on non-linear spectral perturbation BIT 39 1999 350 365
16. L.N. Trefethen Pseudospectra of matrices D.F. Grifiths, G.A. Watson, Numerical Analysis 1992 Longman 234 266
17. J.H. Wilkinson The Algebraic Eigenvalue Problem 1965 Oxford University Press London
18. J.H. Wilkinson Sensitivity of eigenvalues Utilitas Mathematica 25 1984 5 76
19. J.H. Wilkinson Sensitivity of eigenvalues II Utilitas Mathematica 30 1986 243 286