On the evaluation of selected eigenpairs of large matrices based on function optimization algorithms

Molecular Physics

Volumn 101, Issue 1-2, 2003, Pages 45-51

  Bofill, J M ^a,b   Illas, F ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

^b Secció de Química Orgànica   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; ITERATIVE METHODS; MATRIX ALGEBRA; OPTIMIZATION;

CONFIGURATION INTERACTION; EIGENPAIRS; HESSIAN MATRICE; LARGE SCALE MATRIX DIAGONALIZATION; RATIONAL FUNCTION OPTIMIZATION; TAYLOR TECHNIQUES;

MOLECULAR PHYSICS;

EID: 1542288111     PISSN: 00268976     EISSN: 13623028     Source Type: Journal    
DOI: 10.1080/00268970210162808     Document Type: Article

References (61)

1. Shavitt, I., 1977. Methods of Electronic Structure Theory Edited by:Schaefer, H. F., New York:Plenum Press.
2. Boys, S. F., 1953. Proc. R. Soc. Lond. A, 217:235
3. Parr, R. G., Craig, D. P., and Ross, I. G., 1950. J. chem. Phys., 18:1561
4. Löwdin, P. O., 1960. Rev. mod. Phys., 32:328
5. Szabo, A., and Ostlund, N. S., 1996. Modern Quantum Chemistry New York:Dover.
6. Yoshimine, M., 1973. The Use of Direct Access Devices in Problems Requiring the Reordering of Long Data Lists IBM Corp. Tech. Rep. RJ 555
7. Knowles, P. J., and Handy, N. C., 1984. Chem. Phys. Lett., 111:315 1989, Comput. Phys. Commun54, 75
8. Bauschlicher, C. W., Jr., Langhoff, S. R., and Taylor, P. R., 1990. Adv. chem. Phys., 77:103 and references therein
9. Illas, F., Rubio, J., Ricart, J. M., and Bagus, P. S., 1991. J. chem. Phys., 95:1877
10. Zarrabian, S., Sarma, C. S., and Paldus, J., 1989. Chem. Phys. Lett., 155:183
11. Parlett, B. N., 1980. The Symmetric Eigenvalue Problem Englewood Cliffs, NJ:Prentice-Hall.
12. Roos, B., 1972. Chem. Phys. Lett., 15:153
13. Roos, B. O., and Siegbahn, P. E. M., 1977. Methods of Electronic Structure Theory Edited by:Schaefer, H. F., New York:Plenum Press.
14. Ritz, W., 1909. J. Rein. angew. Math., 135:1
15. Galerkin, B. G., 1915. Vestnik Ing., 1:897
16. Hulme, B. L., 1972. Math. Comput., 26:881
17. Saad, Y., 1992. Numerical Methods for Large Eigenvalue Problems New York:Manchester University Press. (Halsted Press, Wiley)
18. Hylleraas, E. A., and Undheim, B., 1930. Z. Phys., 65:759
19. MacDonald, J. K. L., 1933. Phys. Rev., 43:830
20. Lanczos, C., 1950. J. Res. Natl Bur. Stand., 45:255
21. Lanczos, C., 1952. J. Res. Natl Bur. Stand., 49:33
22. Karush, W., 1951. Pacif. J. Math., 1:233
23. Shavitt, I., Bender, C. F., Pipano, A., and Hosteny, R. P., 1973. J. comput. Phys., 11:90
24. van Lenthe, J. H., and Pulay, P., 1990. J. comput. Chem., 11:1164
25. Bofill, J. M., and Anglada, J. M., 1994. Chem. Phys., 183:19
26. Sleijpen, G. L. G., and van der Vorst, H. A., 1994. SIAM J. Matrix Anal. Appl., 17:401
27. Mitin, A. V., 1994. J. comput. Chem., 15:747
28. Hestenes, M. R., 1980. Conjugates Direction Methods in Optimization New York:Springer.
29. Davidson, E. R., 1975. J. comput. Phys., 17:87
30. Davidson, E. R., 1980. J. Phys. A, 13:L179
31. Davidson, E. R., 1989. Comput. Phys. Commun., 53:49
32. Murray, C. W., Racine, S. C., and Davidson, E. R., 1992. J. comput. Phys., 103:382
33. McWeeny, R., 1978. Methods of Molecular Quantum Mechanics, 2nd Edn London:Academic Press.
34. Nesbet, R. K., 1965. J. chem. Phys., 43:311
35. Olsen, J., Jørgensen, P., and Simons, J., 1990. Chem. Phys. Lett., 169:463
36. Besalú, E., and Carbó-Dorca, R., 1997. J. math. Chem., 21:395
37. Besalú, E., and Bofill, J. M., 1998. J. comput. Chem., 19:1777
38. Feler, M. G., 1974. J. comput. Phys., 14:341
39. Wood, D. M., and Zunger, A., 1985. J. Phys. A, 18:1343 Math Gen
40. Huang, Y., Hoffman, D. K., and Kouri, D. J., 1999. J. chem. Phys., 110:8303
41. Buenker, R. J., Peyerimhoff, S. D., and Butcher, W., 1978. Molec. Phys., 35:771
42. Anglada, J. M., Besalú, E., and Bofill, J. M., 1999. Theoret. Chem. Accounts, 103:163
43. Bofill, J. M., Moreira, I. de P. R., Anglada, J. M., and Illas, F., 2000. J. comput. Chem., 21:1375
44. Courant, R., and Hilbert, D., 1953. Methods of Mathematical Physics Vol. 1, New York:Wiley.
45. Shilov, G. E., 1977. Linear Algebra New York:Dover.
46. Carbó, R., and Hernández, J. A., 1976. Introducción a la Teoría de Matrices Madrid:Alhambra.
47. Simons, J., Jørgensen, P., Taylor, J., and Ozment, J., 1983. J. phys. Chem., 87:2745
48. Benerjee, A., Adams, N., Simons, J., and Shepard, K., 1985. J. phys. Chem., 89:52
49. Khait, Y. G., Panin, A. Y., and Averyanov, A. S., 1995. Intl J. quantum Chem., 54:329
50. Besalú, E., and Bofill, J. M., 1998. Theoret. Chem. Accounts, 100:265
51. Fletcher, R., 1987. Practical Methods of Optimization New York:Wiley.
52. Raffenetti, R. C., 1979. J. comput. Phys., 32:403
53. Moreira, I. de P. R., and Illas, F., 1997. Phys. Rev. B, 55:4129
54. Moreira, I., De, P. R., Suaud, N., Guilhery, N., Malrieu, J. P., Caballol, R., Bofill, J. M., and Illas, F., Phys. Rev. B, in press
55. Hestenes, M. R., and Karush, W., 1951. J. Res. Natl Bur. Stand., 47:4, 471
56. Hestenes, M. R., 1980. Conjugate Direction Methods in Optimization New York:Springer.
57. Anglada, J. M., Bofill, J. M., Moreira, I. de P. R., and Illas, F., 2000. Chem. Phys. Lett., 329:160
58. Malrieu, J. P., and Durand, Ph., 1987. Adv. chem. Phys., 67:321
59. Calzado, C. J., and Malrieu, J. P., 2001. Phys. Rev. B, 63:214520
60. Calzado, C. J., Cabrero, J., Caballol, R., and Malrieu, J. P., 2002. J. chem. Phys., 116:3985
61. Moreira, I. de P. R., 2001. Ph. D. thesis, Universitat de Barcelona