A parallel Lanczos method for symmetric generalized eigenvalue problems

Computing and Visualization in Science

Volumn 2, Issue 1, 1999, Pages 37-46

  Wu, Kesheng ^a   Simon, Horst ^a  

^a LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LEARNING ALGORITHMS; PARALLEL ARCHITECTURES;

EXTREME EIGENVALUES; GENERALIZED EIGENVALUE PROBLEMS; LANCZOS ALGORITHM; NUMERICAL EXPERIMENTS; PARALLEL EFFICIENCY; PARALLEL MACHINE; PARTIAL REORTHOGONALIZATION; SYMMETRIC MATRICES;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 33645445695     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s007910050025     Document Type: Article

References (21)

1. Anderson, E., Bai, Z., Bischof, C., Demmel, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A, Ostrouchov, S., Sorensen, D.: LAPACK User's Guide. (SIAM, Philadelphi 1992)
2. Balay, S., Gropp,W., McInnes, L.C., Smith, B.: PETSc 2.0 users manual. Technical Report ANL-95=11. Mathematics and Computer Science Division. Argonne National Laboratory, 1995. Latest source code available at URL http://www.mcs.anl.gov/petsc
3. Chatelin, F.: Eigenvalues of Matrices. (Wiley, New York 1993)
4. Cullum, J., Willoughby, R.A.: Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Programs. Vol. 4 of Progress in Scientific Computing. (Birkhauser, Boston 1985)
5. Cullum, J., Willoughby, R.A.: Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Theory. Vol. 3 of Progress in Scientific Computing. (Birkhauser, Boston 1985)
6. Duff, I.S., Erisman, A.M., Reid, J.K.: Direct Methods for Sparse matrices. (Oxford University Press, Oxford 1986)
7. Duff, I.S., Grimes, R.G., Lewis, J.G.: Sparse matrix test problems. ACM Trans. Math. Soft. 15, 1-14 (1989)
8. Golub, G.H., van Loan, C.F.: Matrix Computations. (The John Hopkins University Press, Baltimore 1996) third Edn.
9. Grimes, R.G., Lewis, J.G., Simon, H.D.: A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems. SIAM J. Matrix Anal. Appl.. 15(1), 228-272 (1994)
10. Hutchinson, S.A., Shadid, J.N., Tuminaro, R.S.: AZTEC user's guide. Technical Report SAND95-1559. (Sandia National Laboratories, Albuquerque 1995)
11. Jones, M.T., Plassmann, P.E.: Blocksolve95 users manual: scalable library software for parallel solution of sparse linear systems. Technical Report ANL-95=48. Mathematics and Computer Science Division. (Argonne national laboratory, Argonne 1995)
12. Lehoucq, R., Sorensen, D., Yang, C.: ARPACK USERS GUIDE: solution of large scale eigenvalue problems with implicitly restarted Arnoldi methods. (SIAM, Philadelphia 1998). ARPACK Software is available at http://www.caam.rice. edu/software/ARPACK/
13. Parlett, B.N., Scott, D.: The Lanczos algorithm with selective orthogonalization. Math. Comp. 33, 217-2388 (1979)
14. Beresford N. Parlett. The symmetric eigenvalue problem. (Prentice- Hall, Englewood Cliffs 1980)
15. Saad, Y., Wu, K.: Design of an iterative solution module for a parallel matrix library (P-SPARSLIB). Applied Numerical Mathematics. 19, 343-357 (1995). Was TR 94-59. Department of Computer Science. University of Minnesota
16. Saad, Y.: Numerical Methods for Large Eigenvalue Problems. (Manchester University Press, Manchester 1993)
17. Saad, Y.: Iterative Methods for Sparse Linear Systems. (PWS Publishing, Boston 1996)
18. Simon H.D.: The Lanczos algorithm for solving symmetric linear systems. PhD thesis. University of California. Berkeley 1982
19. Wang. L.-W, Zunger, A.: Large scale electronic structure calculations using the Lanczos method. Computational Materials Science. 2, 326-340 (1994)
20. Webster, F., Lo, G.-C.: Projective block Lanczos algorithm for dense, Hermitian eigensystems. J. Comput. Phys. 124, 146-161 (1996)
21. Wu, K., Simon, H.: A parallel Lanczos method for symmetric generalized eigenvalue problems. Technical Report 41284, Lawrence Berkeley National Laboratory, 1997. The source code is available from http://www.nersc.gov/ research/SIMON/planso.html