Transfer functions and resolvent norm approximation of large matrices

Electronic Transactions on Numerical Analysis

Volumn 7, Issue , 1998, Pages 190-201

  Simoncini, V ^a   Gallopoulos, E ^b  

^a CNR   (Italy)

^b UNIVERSITY OF PATRAS   (Greece)

Author keywords

Arnoldi iteration; Pseudospectrum; Resolvent norm; Transfer function

Indexed keywords

EID: 0000238118     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. C. BEKAS, I. KOUTIS, V. SIMONCINI AND E. GALLOPOULOS, On transfer functions and approximation of resolvent norms applied to the computation of matrix pseudospectra, Project Inco-Copernicus STABLE Deliverable WP2.2, LHPCA Tech. Rep., Dept. Computer Engineering and Informatics, University of Patras, in preparation.
2. T. BRACONNIER, Complete iterative method for computing pseudospectra, Tech. Rep. 97-13, CERFACS, Toulouse, May 1997.
3. T. BRACONNIER AND N. HIGHAM, Computing the field of values and pseudospectra using the Lanczos method with continuation, BIT 36 (1996), pp. 422-440.
4. J. CARPRAUX, J. ERHEL, AND M. SADKANE, Spectral portrait of non-Hermitian large sparse matrices, Computing, 53 (1994), pp. 301-310.
5. F. CHAITIN-CHATELIN AND V. FRAYSSÉ, Lectures on Finite Precision Computations, SIAM, Philadelphia, 1996.
6. I. DUFF, R. GRIMES, AND J. LEWIS, User's guide for the Harwell-Boeing sparse matrix collection (release I), Tech. Rep. TR/PA/92/86, CERFACS, Toulouse Cedex, France, Oct. 1992.
7. S. GODUNOV, Spectral portraits of matrices and criteria for spectrum dichotomy, in Computer Arithmetic and Enclosure Methods: Proc. Third IMACS-GAMM Symp. Computer Arithmetic and Scientific Computing (SCAN-91), L. Atanassova and J. Herzberger, eds., Amsterdam, 1992, North-Holland.
8. G. GOLUB, F. LUK, AND M. OVERTON, A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix, ACM Trans. Math. Software, 7 (1981), pp. 149-169.
9. J. F. GRCAR, Operator coefficient methods for linear equations, Tech. Rep. SAND89-8691, Sandia National Laboratories, Livermore, CA, 1989.
10. V. HEUVELINE, B. PHILIPPE, AND M. SADKANE, Parallel computation of spectral portrait of large matrices by Davidson type methods, Numer. Algorithms, 16 (1998), pp. 55-75.
11. N. HIGHAM, The Test Matrix Toolbox for MATLAB (version 3.0), Tech. Rep. 276, Manchester Centre for Computational Mathematics, Sept. 1995.
12. D. HINRICHSEN AND A. PRITCHARD, Real and complex stability radii: a survey, in Control of Uncertain Systems, D.Hinrichsen and B. Mårtensson, eds., Birkhäuser, Boston, 1990.
13. R. A. HORN AND C. R. JOHNSON, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
14. P. LAVALLÉE AND M. SADKANE, Une méthode stable de bloc-diagonalisation de matrices: Application au calcul de portrait spectral, Tech. Rep. 3141, INRIA, Rennes, 1997.
15. O. MARQUES AND V. TOUMAZOU, Spectral portrait computation by a Lanczos method, Tech. Rep. PA/95/05, CERFACS, Toulouse, 1995.
16. A. RUHE, The rational Krylov algorithm for large nonsymmetric eigenvalues - mapping the resolvent norms (pseudospectrum), unpublished notes.
17. K. C. TOH, Matrix approximation problems and nonsymmetric iterative methods, Ph.D. thesis, Cornell University, August 1996.
18. K.-C. TOH AND L. TREFETHEN, Calculation of pseudospectra by the Arnoldi iteration, SIAM J. Sci. Comput., 17 (1996), pp. 1-15.
19. L. TREFETHEN, Pseudospectra of matrices, in Numerical Analysis 1991, Proc. 14th Dundee Conf., D. Griffiths and G. Watson, eds., Essex, UK: Longman Sci. and Tech., 1991, pp. 234-266.
20. L. TREFETHEN, A. TREFETHEN, S. REDDY, AND T. DRISCOLL, Hydrodynamic stability without eigenvalues, Science, 261 (July 1993), pp. 578-584.