About Hölder condition numbers and the stratification diagram for defective eigenvalues

Mathematics and Computers in Simulation

Volumn 54, Issue 4-5, 2000, Pages 397-402

  Chaitin Chatelin, F ^a   Harrabi, A ^a   Ilahi, A ^a  

^a UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Exact arithmetic; Finite precision arithmetic; Fr chet and Gateaux derivatives; H lder condition number; Index; Multiple defective eigenvalue; Stratification associated with the commutator AX XA

Indexed keywords

EID: 0347997394     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4754(00)00178-6     Document Type: Article

References (18)

1. V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (1971) 29-43.
2. F. Chaitin-Chatelin, Eigenvalues of Matrices, Wiley, New York, 1993.
3. F. Chaitin-Chatelin, V. Frayssé, Lectures on Finite Precision Computations, SIAM, Philadelphia, PA, 1996.
4. F. Chaitin-Chatelin, V. Frayssé, T. Braconnier, Computations in the neighbourhood of algebraic singularities, Num. Funct. Anal. Opt. 16 (1995) 287-302.
5. F. Chatelin, Spectral Approximation of Linear Operators, Academic Press, New York, 1983.
6. F. Chatelin, Ill-conditioned eigenproblems, in: J. Cullum, R.A. Willoughby (Eds.), Large Scale Eigenvalue Problems, North-Holland, Amsterdam, 1986, pp. 267-282.
7. F. Chatelin, Valeurs propres de matrices, Masson, Paris, 1988.
8. F. Chatelin, Résolution approchée d'équations sur ordinateur. Notes de DEA, Université Paris VI, 1989.
9. A. Harrabi, About Holder condition numbers of Gateaux and Fréchet type for general nonlinear functions, Manuscript -CERFACS, 1998.
10. A. Harrabi, Pseudospectres d'opérateurs intégraux et différentiels: application à la physique mathématique, Ph.D. Thesis, Université des Sciences Sociales, Toulouse I, 1998.
11. A. Harrabi, Défaut de Normalité. Technical report, CERFACS, TR/PA/98/36.
12. A. Ilahi, Validation du calcul sur ordinateur: application de la théorie des singularités, Ph.D. Thesis, Université des Sciences Sociales, Toulouse I, 1998.
13. T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1976.
14. V.B. Lidskii, Perturbation theory of non-conjugate operators, U.S.S.R. Comput. Math. Phys. 1 (1965) 73-85.
15. R.A. McCoy, V Toumazou, PRECISE User's Guide - Version 1.0. Technical report, CERFACS, TR/PA/97/38.
16. J. Moro, J.V Burke, M.L. Overton, On the Lidskii-Vishik-Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure, SIAM J. Matrix Anal. Appl. 18 (1997) 793-817.
17. V. Puiseux, Recherches sur les fonctions algébriques, J. Math. Pures Appl. 51 (1850) 465-581.
18. J.R. Rice, A theory of condition, J. SIAM Numer. Anal. 3 (2) (1966) 287-310.