Nonlinear sequence transformations: A computational tool for quantum mechanical and quantum chemical calculations

International Journal of Quantum Chemistry

Volumn 57, Issue 3, 1996, Pages 265-280

  Weniger, Ernst Joachim ^a  

^a UNIVERSITY OF REGENSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001407401     PISSN: 00207608     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-461X(1996)57:3<265::AID-QUA1>3.0.CO;2-W     Document Type: Article

References (71)

1. K. Knopp, Theorie und Anwendung der unendlichen Reihèn (Springer-Verlag, Berlin, 1964).
2. C. Brezinski, History of Continued Fractions and Padé Approximants (Springer-Verlag, Berlin, 1991).
3. L. F. Richardson, Philos. Trans. R. Soc. Lond. A 226, 229 (1927).
4. A. C. Aitken, Proc. R. Soc. Edinb. 46, 289 (1926).
5. G. H. Hardy, Divergent Series (Clarendon Press, Oxford, 1949).
6. G. M. Petersen, Regular Matrix Transformations (McGraw-Hill, London, 1966).
7. A. Peyerimhoff, Lectures on Summability (Springer-Verlag, Berlin, 1969).
8. R. E. Powell, and S. M. Shah, Summability Theory and Its Applications (Prentice-Hall of India, New Delhi, 1988).
9. J. Wimp, Sequence Transformations and Their Applications (Academic Press, New York, 1981).
10. P. Wynn, Math. Tables Aids Comput. 10, 91 (1956).
11. P. Wynn, Proc. Camb. Philos. Soc. 52, 663 (1956).
12. C. Brezinski, C. R. Acad. Sci. Paris 273, 727 (1971).
13. C. Brezinski, Acceleration de la Convergence en Analyse Numérique (Springer-Verlag, Berlin, 1977).
14. C. Brezinski, Algorithmes d'Accélération de la Convergence - Étude Numérique (Editions Technip, Paris, 1978).
15. C. Brezinski, Padé-Type Approximation and General Orthogonal Polynomials (Birkhäuser, Basel, 1980).
16. C. Brezinski and M. Redivo Zaglia, Extrapolation Methods (North-Holland, Amsterdam, 1991).
17. A. Cuyt and L. Wuytack, Nonlinear Methods in Numerical Analysis (North-Holland, Amsterdam, 1987).
18. J.-P Delahaye, Sequence Transformations (Springer-Verlag, Berlin, 1988).
19. A. J. Guttmann, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, Eds. (Academic Press, London, 1989), Vol. 13, p. 3.
20. E. J. Weniger, Comput. Phys. Rep. 10, 189 (1989).
21. G. A. Baker, Jr., Essentials of Padé Approximants (Academic Press, New York, 1975).
22. G. A. Baker, Jr. and P. Graves-Morris, Padé Approximants. Part I: Basic Theory. Part II: Extensions and Applications (Addison-Wesley, Reading, MA, 1981).
23. E. J. Weniger, J. Comput. Appl. Math. 32, 291 (1990).
24. E. J. Weniger, J. Čížek, and F. Vinette, Phys. Lett. A 156, 169 (1991).
25. E. J. Weniger, Numer. Algor. 3, 477 (1992).
26. E. J. Weniger, J. Čížek, and F. Vinette, J. Math. Phys. 34, 571 (1993).
27. E. J. Weniger, Verallgemeinerte Summationsprozesse als numerische Hilfsmittel für quantenmechanische und quantenchemische Rechnungen (Habilitationsschrift, Universität Regensburg, 1994). Compressed .dvi and .ps files can be obtained via anonymous ftp from directory /pub/preprint/Weniger/habil of rchs1.chemie.uni-regensburg.de (IP 132.199.48.1).
28. B. C. Carlson, Special Functions of Applied Mathematics (Academic Press, New York, 1977).
29. D. Levin, Int. J. Comput. Math. B 3, 371 (1973).
30. C. Schneider, Numer. Math. 24, 177 (1975).
31. C. Brezinski, Numer. Math. 35, 175 (1980).
32. T. Håvie, BIT 19, 204 (1979).
33. E. J. Weniger, Comput. Phys. Commun. 64, 19 (1991).
34. C. Brezinski and M. Redivo Zaglia, Advances Comput. Math. 2, 461 (1994).
35. C. Brezinski and M. Redivo Zaglia, Appl. Numer. Math., in press.
36. C. Brezinski and A. C. Matos, J. Comput. Appl. Math., in press.
37. D. A. Smith and W. F. Ford, SIAM J. Numer. Anal. 16, 223 (1979).
38. D. A. Smith and W. F. Ford, Math. Comput. 38, 481 (1982).
39. H. H. H. Homeier, Int. J. Quantum Chem. 45, 545 (1993).
40. H. H. H. Homeier, Numer. Algor. 8, 47 (1994).
41. H. H. H. Homeier, J. Comput. Appl. Math., in press.
42. H. H. H. Homeier, Numer. Math., in press.
43. A. Sidi, Math. Comput. 33, 315 (1979).
44. A. Sidi, Math. Comput. 35, 833 (1980).
45. A. Sidi, SIAM J. Math. Anal. 17, 1222 (1986).
46. M. Reed and B. Simon, Methods of Modern Mathematical Physics IV: Analysis of Operators (Academic Press, New York, 1978).
47. J. Killingbeck, Rep. Prog. Phys. 40, 963 (1977).
48. G. A. Arteca, F. M. Fernández, and E. A. Castro, Large Order Perturbation Theory and Summation Methods in Quantum Mechanics (Springer-Verlag, Berlin, 1990).
49. C. M. Bender and T. T. Wu, Phys. Rev. 184, 1231 (1969).
50. C. M. Bender and T. T. Wu, Phys. Rev. Lett. 27, 461 (1971).
51. C. M. Bender and T. T. Wu, Phys. Rev. D 7, 1620 (1973).
52. P.-O. Löwdin, Ed., Proceedings of the Sanibel Workshop on Perturbation Theory at Large Order, Sanibel Conference, Florida, 1981, Int. J. Quantum Chem. 21, 1 (1982).
53. J. C. Le Guillou and J. Zinn-Justin, Eds., Large-Order Behaviour of Perturbation Theory (North-Holland, Amsterdam, 1990).
54. B. G. Adams, Algebraic Approach to Simple Quantum Systems (Springer-Verlag, Berlin, 1994).
55. B. Simon, Ann. Phys. (NY) 58, 76 (1970).
56. B. Simon, Int. J. Quantum Chem. 21, 3 (1982).
57. S. Graffi and V. Grecchi, J. Math. Phys. 19, 1002 (1978).
58. J. Čížek and E. R. Vrscay, Int. J. Quantum Chem. 21, 27 (1982).
59. F. Vinette and J. Čížek, J. Math. Phys. 32, 3392 (1991).
60. B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, Maple V Language Reference Manual (Springer-Verlag, Berlin, 1991).
61. F. T. Hioe and E. W. Montroll, J. Math. Phys. 16, 1945 (1975).
62. F. T. Hioe, D. MacMillen, and E. W Montroll, Phys. Rep. 43, 305 (1978).
63. A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988).
64. F. M. Fernández, Phys. Lett. A 166, 173 (1992).
65. R. Guardiola, M. A. Solís, and J. Ros, II Nuovo Cimento B 107, 713 (1992).
66. K. Bhattacharyya, Int. J. Quantum Chem. 22, 307 (1982).
67. K. Bhattacharyya, Proc. Indian Acad. Sci (Chem. Sci.) 99, 9 (1987).
68. J. N. Silverman, Phys. Rev. A 28, 498 (1983).
69. T. Ćwiok, B. Jeziorski, W. Kolos, R. Moszynski, J. Rychlewski, and K. Szalewicz, Chem. Phys. Lett. 195, 67 (1992).
70. R. E. Shafer, SIAM J. Numer. Anal. 11, 447 (1974).
71. S. L. Loi and A. W. McInnes, J. Comput. Appl. Math. 11, 161 (1984).