Programs for the approximation of real and imaginary single- and multi-valued functions by means of Hermite-Padé-approximants

Computer Physics Communications

Volumn 158, Issue 2, 2004, Pages 124-135

  Feil, T M ^a   Homeier, H H H ^a,b  

^a UNIVERSITY OF REGENSBURG   (Germany)

^b Science + Computing ag   (Germany)

Author keywords

Anharmonic oscillators; Convergence acceleration; Extrapolation; Perturbation theory; Summation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER PROGRAMMING LANGUAGES; DATA REDUCTION; FUNCTIONS; POLYNOMIALS; QUANTUM THEORY; VECTORS;

IDENTIFIERS; MULTI-VALUED FUNCTIONS;

COMPUTER PROGRAM LISTINGS;

EID: 1642293502     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2004.02.002     Document Type: Article

References (34)

1. Löwdin P.O. Proceedings of the Sanibel workshop on perturbation theory at large order, Sanibel Conference, Florida, 1981. Int. J. Quantum Chem. 21:1982;1-209.
2. Le Guillou J.C., Zinn-Justin J. Large-Order Behaviour of Perturbation Theory. 1990;North-Holland, Amsterdam.
3. Padé H. Sur la généralisation des fractions continues algébriques. J. Math. Pures Appl. 10:1894;291-329.
4. Borel E. Mémoires sur les séries divergentes. Ann. Sci. Ec. Norm. Sup. Paris. 16:1899;9-136.
5. Baker G.A. Jr., Graves-Morris P. Padé Approximants. second edition: 1996;Cambridge Univ. Press, Cambridge, GB.
6. Sergeev A.V. Summation of the eigenvalue perturbation series by multi-valued Padé approximants: application to resonance problems and double wells. J. Phys. A: Math. Gen. 28:1995;4157-4162.
7. Sergeev A.V., Goodson D.Z. Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: application to anharmonic oscillators. J. Phys. A: Math. Gen. 31:1998;4301-4317.
8. T. Feil, Anwendung von Ein- und Mehrreihen-Hermite-Padé-Approximationsverfahren zur Summation divergenter Störungsreihen, Diploma Thesis, University of Regensburg, Germany, 2000.
9. Goodson D.Z. Convergent summation of Møller-Plesset perturbation theory. J. Chem. Phys. 112:(11):2000;4901-4909.
10. P. Bracken, Interpolant polynomials in quantum mechanics and study of the one dimensional Hubbard model, Ph.D. Thesis, University of Waterloo, 1994.
11. Bracken P., Čížek J. Construction of interpolant polynomials for approximating eigenvalues of a Hamiltonian which is dependent on a coupling constant. Phys. Lett. A. 194:1994;337-342.
12. - states in cyclic polyenes. Int. J. Quantum Chem. 53:1995;467-471.
13. Bracken P., Čížek J. Interpolant polynomial technique applied to the PPP model. I. Asymptotics for excited states of cyclic polyenes in the finite cyclic Hubbard model. Int. J. Quantum Chem. 57:1996;1019-1032.
14. Čížek J., Bracken P. Interpolant polynomial technique applied to the PPP model. II. Testing the interpolant technique on the Hubbard model. Int. J. Quantum Chem. 57:1996;1033-1048.
15. Downing J.W., Michl J., Čížek J., Paldus J. Multidimensional interpolation by polynomial roots. Chem. Phys. Lett. 67:1979;377-380.
16. Takahashi M., Bracken P., Čížek J., Paldus J. Perturbation expansion of the ground state energy for the one-dimensional cyclic Hubbard system in the Hückel limit. Int. J. Quantum Chem. 53:1995;457-466.
17. Čížek J., Weniger E.J., Bracken P., Špirko V. Effective characteristic polynomials and two-point Padé approximants as summation techniques for the strongly divergent perturbation expansions of the ground state energies of anharmonic oscillators. Phys. Rev. E. 53:1996;2925-2939.
18. H.H.H. Homeier, Extrapolationsverfahren für Zahlen-, Vektor- und Matrizenfolgen und ihre Anwendung in der Theoretischen und Physikalischen Chemie, Habilitation Thesis, University of Regensburg, Germany, 1996.
19. Homeier H.H.H. Correlation energy estimators based on Møller-Plesset perturbation theory. J. Mol. Struct. (Theochem). 366:1996;161-171.
20. Homeier H.H.H. The size-extensivity of correlation energy estimators based on effective characteristic polynomials. J. Mol. Struct. (Theochem). 419:1997;29-31. Proceedings of the 3rd Electronic Computational Chemistry Conference.
21. Homeier H.H.H., Neef M.D. Performance of the effective-characteristic-polynomial Π2 method for diatomic molecules: Basis-set dependencies and vibrational levels. Internet J. Chem. 3:2000;. (Article 5) Online computer file: http://www.ijc.com/articles/2000v3/5/ . Proceedings of the 5th Electronic Computational Chemistry Conference.
22. Homeier H.H.H. On the extrapolation of perturbation series. Acta Appl. Math. 61:(1/3):2000;133-147 Homeier H.H.H. On the extrapolation of perturbation series. Cuyt A. Proceedings of the International Conference on Rational Approximation (ICRA99), Antwerpen, Belgium. 1999.
23. Homeier H.H.H. On the extrapolation of perturbation series. Acta Appl. Math. 61:(1/3):2000;133-147 Homeier H.H.H. On the extrapolation of perturbation series. Cuyt A. Proceedings of the International Conference on Rational Approximation (ICRA99), Antwerpen, Belgium. 1999.
24. Sergeev A. A recursive algorithm for Padé-Hermite approximations. Comput. Math. Math. Phys. 26:(2):1986;17-22. Engl. transl.
25. Hermite C. Sur la généralisation des fractions continues algébriques. Ann. Math. Pura Appl. 21:1893;289-308.
26. Bender C.M., Orszag S.A. Advanced Mathematical Methods for Scientists and Engineers. 1978;McGraw-Hill, New York.
27. Char B.W., Geddes K.O., Gonnet G.H., Leong B.L., Monagan M.B., Watt S.M. Maple V Language Reference Manual, Berlin. 1991.
28. Char B.W., Geddes K.O., Gonnet G.H., Leong B.L., Monagan M.B., Watt S.M. Maple V Library Reference Manual, Berlin. 1991.
29. Wolfram S. Mathematica: A system for Doing Mathematics by Computer. 1991;Addison-Wesley, Redwood City, CA.
30. Bender C.M., Wu T.T. Anharmonic oscillator. Phys. Rev. 184:1969;1231-1260.
31. Simon B. Coupling constant analyticity for the anharmonic oscillator. Ann. Phys. 58:1970;76-136.
32. M perturbation. J. Phys. A. 13:1980;49-56.
33. Weniger E.J. A convergent renormalized strong coupling perturbation expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator. Ann. Phys. 246:1996;133-165.
34. Arteca G.A., Fernández F.M., Castro E.A. Large Order Perturbation Theory and Summation Methods in Quantum Mechanics. 1990;Springer, Berlin.