Computation of pseudospectra via spectral projectors

Linear Algebra and Its Applications

Volumn 279, Issue 1-3, 1998, Pages 163-175

  Godunov, S K ^a   Sadkane, M ^b  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

^b UFR SCIENCES ET TECHNIQUES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042095006     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(98)00011-1     Document Type: Article

References (24)

1. Z. Bai, J. Demmel, M. Gu, Inverse free parallel spectral divide and conquer algorithms for nonsymmetric eigenproblems, Computer Science Division Report UCB/CSD-94-793, University of California, Berkeley, CA, 1994.
2. T. Braconnier, N.J. Higham, Computing the field of values and pseudospectra using the Lanczos method with continuation, BIT 36 (3) (1996) 422-440.
3. M. Brühl, A curve tracing algorithm for computing the pseudospectrum, BIT 36 (3) (1996) 441-454.
4. A.Y. Bulgakov, S.K. Godunov, Circular dichotomy of the spectrum of a matrix, Siberian Math. J. 29 (1988) 734-744.
5. J.F. Carpraux, J. Erhel, M. Sadkane, Spectral portrait for non hermitian large matrices, Computing 53 (1994) 301-310.
6. V. Frayssé, L. Giraud, V. Toumazou, Parallel computation of spectral portraits on the Meiko CS2, in: H. Liddel, A. Colbrook, B. Hertzberger, P. Sloot (Eds.), High-Performance Computing and Networking, vol. 1067, Springer, Berlin, 1996, pp. 312-318.
7. S.K. Godunov, Problem of the dichotomy of the spectrum of a matrix, Siberian Math. J. 27 (1986) 649-660.
8. S.K. Godunov, O.P. Kiriljuk, V.I. Kostin, Spectral portrait of matrices (Russian), AN SSSR Siber. Otd. Novosibirsk preprint, 1990.
9. S.K. Godunov, M. Sadkane, Elliptic dichotomy of a matrix spectrum, Linear Algebra Appl. 248 (1996) 205-232.
10. G.H. Golub, Ch. Van Loan, Matrix Computation, 2nd ed., Johns Hopkins University Press, Baltimore, MD, 1989.
11. V. Heuveline, M. Sadkane, Parallel computation of spectral portrait of large matrices, in: The Third International Workshop on Applied Parallel Computing in Industrial Problems and Optimization (PARA96), Lyngby, Denmark, 18-21 August 1996; J. Dongarra et al. (Eds.), Lecture Notes in Computer Science series, vol. 1184, Springer, Berlin, pp. 398-407.
12. N.J. Higham, The Test Matrix Toolbox for Matlab (version 3.0), Technical Report, Manchester Centre for Computational Mathematics, 1995.
13. R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, MA, 1991.
14. T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1976.
15. P.-F. Lavallée, M. Sadkane, Une méthode stable de bloc-diagonalisation de matrices, Application au calcul de portrait spectral, Rapport de Recherche INRIA no. 3141, 1997.
16. S.H. Lui, Computation of pseudospectra by continuation, SIAM J. Sci. Comput. 18 (2) (1997).
17. A.N. Malyshev, Parallel algorithm for solving some spectral problems of linear algebra, Linear Algebra Appl. 188/189 (1993) 489-520.
18. A.N. Malyshev, M. Sadkane, On parabolic and elliptic spectral dichotomy, SIAM J. Matrix Anal. Appl. 18 (2) (1997).
19. B. Philippe, M. Sadkane, Computation of the fundamental singular subspace of a large matrix, Linear Algebra Appl. 257 (1997) 77-104.
20. G. Stewart, J. Sun, Matrix Perturbation Theory, Academic Press, San Diego, CA, 1990.
21. K.-C. Toh, L.N. Trefethen, Calculation of pseudospectra by the Arnoldi method, SIAM J. Sci. Comput. 17 (1996) 1-15.
22. V. Toumazou, Portrait spectraux de matrices: Un outil d'analyse de la stabilité, Ph.D. Thesis, Université H. Poincaré, Nancy, 1996.
23. L.N. Trefethen, Pseudospectra of matrices, in: D.F. Griffiths, G.A. Watson (Eds.), Proceedings of the 14th Dundee Biennial Conference on Numerical Analysis, 1991.
24. L.N. Trefethen, Pseudospectra of linear operators, in: Proceedings of the Third International Congress on Industrial and Applied Mathematics, 1995 (ICIAM'95), Akademie, Berlin.