Calculation of clustered eigenvalues of large matrices using variance minimization method

Journal of Computational Chemistry

Volumn 19, Issue 15, 1998, Pages 1777-1785

  Besalú, Emili ^a   Bofill, Josep Maria ^b  

^a UNIVERSITY OF GIRONA   (Spain)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Clustered eigenvalues; Large matrices; Variance minimization method

Indexed keywords

EID: 0039480952     PISSN: 01928651     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1096-987X(19981130)19:15<1777::AID-JCC9>3.0.CO;2-K     Document Type: Article

References (32)

1. I. Shavitt, In Methods of Electronic Structure Theory, H. F. Schaefer III, Ed., Plenum, New York, 1977, p. 189.
2. (a) W. Ritz, J. Rein. Angew. Math., 135, 1 (1909)
3. (b) B. G. Galerkin, Vestnik Ing., 1, 897 (1915).
4. C. Lanczos, J. Res. Natl. Bur. Stand., 45, 255 (1950), 49, 33 (1952).
5. C. Lanczos, J. Res. Natl. Bur. Stand., 45, 255 (1950), 49, 33 (1952).
6. W. Karush, Pacif. J. Math., 1, 233 (1951).
7. C. C. Paige, J. Inst. Math. Applic., 18, 341 (1976).
8. B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980.
9. (a) E. R. Davidson, J. Comput. Phys., 17, 87 (1975)
10. (b) E. R. Davidson, J. Phys. A, 13, L179 (1980)
11. (c) E. R. Davidson, Comput. Phys. Commun., 53, 49 (1989)
12. (d) C. W. Murray, S. C. Racine, and E. R. Davidson, J. Comput. Phys., 103, 382 (1992).
13. B. Liu, Report on the Workshop "Numerical Algorithms in Chemistry: Algebraic Methods," of the National Resource for Computation in Chemistry, Lawrence Berkeley Laboratory, 9-11 August, C. Moler and I. Shavitt, Eds., LBL-8158, UC-32, CONF-780878, Lawrence Berkeley Laboratory, Livermore, CA, 1978, p. 49.
14. Y. Saad, Numerical Methods for Large Eigenvalue Problems, Manchester University Press, Halsted Press, Wiley, New York, 1992.
15. J. Olsen, P. Jørgensen, and J. Simons, Chem. Phys. Lett., 169, 463 (1990).
16. J. M. Bofill and J. M. Anglada, Chem. Phys., 183, 19 (1994).
17. J. H. van Lenthe and P. Pulay, J. Comput. Chem., 11, 1164 (1990).
18. A. V. Mitin, J. Comput. Chem., 15, 747 (1994).
19. (a) M. R. Hestenes and E. Stiefel, J. Res. Natl. Bur. Stand., 49, 498 (1952)
20. (b) M. R. Hestenes, Conjugate Direction Methods in Optimization, Springer, New York, 1980.
21. G. A. Gallup, J. Comput. Chem., 3, 127 (1982).
22. L. M. Cheung and D. M. Bishop, Comput. Phys. Commun., 13, 247 (1977).
23. M. G. Feler, J. Comput. Phys., 14, 341 (1974).
24. I. Shavitt, C. F. Bender, A. Pipano, and R. P. Hosteny, J. Comput. Phys., 11, 90 (1973).
25. D. M. Wood and A. Zunger, J. Phys. A Math. Gen., 18, 1343 (1985).
26. (a) P. Pulay, Chem. Phys. Lett., 73, 393 (1980)
27. (b) P. Pulay, J. Comput. Chem., 3, 556 (1982).
28. E. Besalú and R. Carbó-Dorca, J. Math. Chem., 21, 395 (1997).
29. J. Linderberg and Y. Ohrn, Int. J. Quantum Chem., 12, 161 (1977).
30. D. H. Weinstein, Proc. Natl. Acad. Sci., 20, 529 (1934).
31. N. Kosugi, J. Comput. Phys., 55, 426 (1984).
32. R. C. Raffenetti, J. Comput. Phys., 32, 403 (1979).