Parallel preconditioning of a sparse eigensolver

Parallel Computing

Volumn 27, Issue 7, 2001, Pages 963-976

  Bergamaschi, Luca ^a   Pini, Giorgio ^a   Sartoretto, Flavio ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b CA' FOSCARI UNIVERSITY OF VENICE   (Italy)

Author keywords

Generalized eigenproblems; Parallel algorithms; Sparse approximate inverses

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; EIGENVALUES AND EIGENFUNCTIONS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; INVERSE PROBLEMS; PARALLEL ALGORITHMS; PROBLEM SOLVING; SUPERCOMPUTERS;

DEFLATION-ACCELERATED CONJUGATE GRADIENT (DACG);

PARALLEL PROCESSING SYSTEMS;

EID: 0035371089     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8191(01)00077-1     Document Type: Article

References (17)

1. Bathe K.J., Wilson E. Solution methods for eigenvalue problems in structural dynamics. Int. J. Numer. Methods Eng. 6:1973;213-226.
2. Benzi M., Meyer C.D., Tůma M. A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Sci. Comput. 17(5):1996;1135-1149.
3. Bergamaschi L., Gambolati G., Pini G. Asymptotic convergence of conjugate gradient methods for the partial symmetric eigenproblem. Numer. Lin. Alg. Appl. 4(2):1997;69-84.
4. Bergamaschi L., Pini G., Sartoretto F. Approximate inverse preconditioning in the parallel solution of sparse eigenproblems. Numer. Lin. Alg. Appl. 7(3):2000;99-116.
5. L. Bergamaschi, M. Putti, Numerical comparison of iterative methods for the eigensolution of large sparse symmetric matrices, SIAM J. Sci. Comput. June, 2000 (preprint).
6. L. Bergamaschi, M. Putti, Efficient parallelization of preconditioned conjugate gradient schemes for matrices arising from discretizations of diffusion equations, in: Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, March, 1999 (CD-ROM).
7. Ericsson T., Ruhe A. The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems. Math. Comp. 35:1980;1251-1268.
8. Gambolati G., Sartoretto F., Florian P. An orthogonal accelerated deflation technique for large symmetric eigenproblems. Comp. Methods App. Mech. Eng. 94:1992;13-23.
9. Knyazev A.V., Skorokhodov A.L. The preconditioned gradient-type iterative methods in a subspace for partial generalized symmetric eigenvalue problem. SIAM J. Numer. Anal. 31(4):1994;1226-1239.
10. Kolotilina L.Y., Yeremin A.Y. Factorized sparse approximate inverse preconditioning. I theory. SIAM J. Matrix Anal. Appl. 14:1993;45-58.
11. Lanczos C. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Nat. Bur. Standard. 45:1950;255-282.
12. Lehoucq R.B., Sorensen D.C. Deflation techniques for an implicit restarted Arnoldi iteration. SIAM J. Matrix Anal. Appl. 17(4):1996;789-821.
13. Lehoucq R.B., Sorensen D.C., Yang C. ARPACK. Users guide solution of large scale eigenvalue problem with implicit restarted Arnoldi methods. SIAM. 1998.
14. Paige C.C. Computational variants of the Lanczos method for the eigenproblem. J. Inst. Math. Applics. 10:1972;373-381.
15. Parlett B.N. The symmetric eigenvalue problem. 1980;Prentice-Hall, Englewood Cliffs, NJ.
16. Sartoretto F., Pini G., Gambolati G. Accelerated simultaneous iterations for large finite element eigenproblems. J. Comp. Phys. 81:1989;53-69.
17. Sleijpen G.L.G., van der Vorst H.A. A Jacobi-Davidson method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl. 17(2):1996;401-425.