On the sensitivity of some spectral preconditioners

SIAM Journal on Matrix Analysis and Applications

Volumn 27, Issue 4, 2006, Pages 1089-1105

  Giraud, L ^a,b   Gratton, S ^a  

^a CERFACS   (France)

^b UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Coarse grid preconditioned deflating preconditioner; Sensitivity analysis; Spectral preconditioned

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES;

COARSE GRID PRECONDITIONED DEFLATING PRECONDITIONER; SPECTRAL PRECONDITIONED;

SENSITIVITY ANALYSIS;

EID: 33750144297     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/040617546     Document Type: Conference Paper

References (18)

1. R. A. HORN AND C. R. JOHNSON, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1995.
2. J. H. BRAMBLE, J. E. PASCIAK, AND A. H. SCHATZ, The construction of preconditioners for elliptic problems by substructuring I., Math. Comp., 47 (1986), pp. 103-134.
3. B. CARPENTIERI, I. S. DUFF, AND L. GIRAUD, A class of spectral two-level preconditioned,SIAM J. Sci. Comput., 25 (2003), pp. 749-765.
4. B. CARPENTIERI, L. GIRAUD, AND S. GRATTON, Additive and Multiplicative Spectral Two-level Preconditioned for General Linear Systems, Technical Report TR/PA/04/38, CERFACS, Toulouse, France, 2004.
5. T. F. CHAN AND T. P. MATHEW, Domain Decomposition Algorithms, Acta Numer. 3, Cambridge University Press, Cambridge, UK, 1994, pp. 61-143.
6. I. S. DUFF, L. GIRAUD, J. LANGOU, AND E. MARTIN, Using spectral low rank preconditioned for large electromagnetic calculations, Int. J. Numer. Methods Engrg., 62 (2005), pp. 416-434.
7. I. S. DUFF, R. G. GRIMES, AND J. G. LEWIS, Sparse matrix test problems, ACM Trans. Math. Softw., 15 (1989), pp. 1-14.
8. M. FISHER, Minimization algorithms for variational data assimilation, in Proceedings of the ECMWF seminar "Recent developments in numerical methods for atmospheric modelling," Reading, UK, 1998, pp. 364-385.
9. J. FRANK AND C. VUIK, On the construction of deflation-based preconditioners, SIAM J. Sci. Comput., 23 (2001), pp. 442-462.
10. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
11. N. J. HlGHAM, Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM, Philadelphia, 2002.
12. P. LANCASTER AND M. TISMENETSKY, The Theory of Matrices, 2nd ed., Academic Press, New York, 1985.
13. R. NABBEN AND C. VUIK, A comparison of deflation and coarse grid correction applied to porous media flow, SIAM J. Numer. Anal., 42 (2004), pp. 1631-1647.
14. A. PADIY, O. AXELSSON, AND B. POLMAN, Generalized augmented matrix preconditioning approach and its application to iterative solution of ill-conditioned algebraic systems, SIAM J. Matrix Anal. Appl., 22 (2000), pp. 793-818.
15. J. R. RICE, A theory of condition, SIAM J. Numer. Anal., 3 (1966), pp. 287-310.
16. G. W. STEWART, Matrix Algorithms. Volume II: Eigensystems, SIAM, Philadelphia, 2001.
17. J. SUN, Multiple eigenvalue sensitivity, Linear Algebra Appl., 138 (1990), pp. 183-211.
18. [18 H. WAISMAN, J. FISH, R. S. TUMINARO, AND J. SHADID, The generalized global basis method, Int. J. Numer. Methods in Engrg., 61 (2004), pp. 1243-1269.