On the convergence rate of a preconditioned subspace eigensolver

Computing (Vienna/New York)

Volumn 63, Issue 3, 1999, Pages 219-231

  Oliveira, S ^a  

^a University of Iowa   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS;

PRECONDITIONED SUBSPACE EIGENSOLVER;

COMPUTATION THEORY;

EID: 0033354544     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006070050032     Document Type: Article

References (19)

1. Bank, R. E., Sherman, A. H.: An adaptive multi-level method for elliptic boundary value problems Computing 26, 91-105 (1981).
2. Borges, L., Oliveira, S.: A parallel Davidson-type algorithm for several eigenvalues. J. Comput. Phys. 144, 727-748 (1998).
3. Bramble, J. H.: Multigrid methods. Pitman Research Notes in Mathematical Sciences Vol. 294. Essex: Longman 1993.
4. Bramble, J. H., Pasciak, J. E., Knyazev, A. V.: A subspace preconditioning algorithm for eigenvector/eigenvalue computation, Adv. Comput. Math. 6, 159-189 (1996).
5. Crouzeix, M., Philippe, B., Sadkane, M.: The Davidson method. SIAM J. Sci. Comput. 15, 62-76 (1994).
6. Davidson, E. R.: The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J. Comp. Phys. 17, 87-94 (1975).
7. Greenbaum, A.: Iterative methods for solving linear systems. Philadelphia: SIAM 1997.
8. Hackbusch, W.: On the multigrid method applied to difference equations. Computing 20, 291-306 (1978).
9. Hackbusch, W., Wittum, G. (eds.): Incomplete decomposition (ILU) - algorithms, theory, and applications. Braunschweig: Vieweg 1993.
10. Horne, R., Johnson, C.: Matrix analysis. Cambridge: Cambridge University Press 1985.
11. McCormick, S. (ed.): Multigrid methods: Frontiers in Applied Mathematics. Philadelphia: SIAM 1987.
12. Oliveira, S.: A convergence proof of an iterative subspace method for eigenvalues problem. In: Foundations of computational mathematics. Selected papers (Cucker, F., Shub, M., eds.), pp. 316-325. Berlin Heidelberg New York Tokyo: Springer 1997.
13. Olsen, J., Jorgensen, P., Simons, J.: Passing the one-billion limit in full configuration-interaction (FCI) calculations. Chem. Phys. Lett. 169, 463-472 (1990).
14. Parlett, B. N.: The Rayleigh quotient iteration and some generalizations. Math. Comput. 28, 679-693 (1974).
15. Saad, Y.: Numerical methods for large eigenvalue problems: Algorithms and architectures for advanced scientific computing series. New York, Brisbane, Toronto: Manchester University Press and Halsted Press 1992.
16. Sleijpen, G., Van der Vorst, H.: A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl. 17, 401-425 (1996).
17. Wu, K.: Preconditioned techniques for large eigenvalue problems. PhD thesis, University of Minnesota, 1997. (An updated version also appears as Technical Report TR97-038 at the Computer Science Department)
18. Wu, K., Saad, Y., Stathopoulos, A.: Inexact Newton preconditioning techniques for eigenvalue problems. Electr. Trans. Numer. Anal. 7, 202-214 (1998).
19. Yserentant, H.: Old and new convergence proofs for multigrid methods. In: Acta Numerica (Iserles, A., ed.), pp. 285-326. Cambridge: Cambridge University Press 1993.