메뉴 건너뛰기




Volumn 61, Issue 1-3, 2000, Pages 133-147

On the Extrapolation of Perturbation Series

Author keywords

Algebraic approximants; Anharmonic oscillators; Convergence acceleration; Effective characteristic polynomials; Extrapolation; Multiseries approximants; Perturbation theory; Quantum mechanics; Summation of divergent series

Indexed keywords


EID: 0041723624     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1006493830706     Document Type: Article
Times cited : (4)

References (32)
  • 3
    • 36049055534 scopus 로고
    • Anharmonic oscillator
    • Bender, C. M. and Wu, T. T.: Anharmonic oscillator, Phys. Rev. 184 (1969), 1231-1260.
    • (1969) Phys. Rev. , vol.184 , pp. 1231-1260
    • Bender, C.M.1    Wu, T.T.2
  • 4
    • 5344255945 scopus 로고
    • Large-order behavior of perturbation theory
    • Bender, C. M. and Wu, T. T.: Large-order behavior of perturbation theory, Phys. Rev. Lett. 27 (1971), 461-465.
    • (1971) Phys. Rev. Lett. , vol.27 , pp. 461-465
    • Bender, C.M.1    Wu, T.T.2
  • 5
    • 7044255672 scopus 로고
    • Anharmonic oscillator. II. A study in perturbation theory in large order
    • Bender, C. M. and Wu, T. T.: Anharmonic oscillator. II. A study in perturbation theory in large order, Phys. Rev. D 7 (1973), 1620-1636.
    • (1973) Phys. Rev. D , vol.7 , pp. 1620-1636
    • Bender, C.M.1    Wu, T.T.2
  • 6
    • 0000905803 scopus 로고    scopus 로고
    • 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
    • Čížek, J., Weniger, E. J., Bracken, P. and 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.
    • (1996) Phys. Rev. e , vol.53 , pp. 2925-2939
    • Čížek, J.1    Weniger, E.J.2    Bracken, P.3    Špirko, V.4
  • 7
    • 0034289858 scopus 로고    scopus 로고
    • Scalar Levin-type sequence transformations
    • Invited review for in press
    • Homeier, H. H. H.: Scalar Levin-type sequence transformations, Invited review for J. Comput. Appl. Math., in press.
    • J. Comput. Appl. Math.
    • Homeier, H.H.H.1
  • 8
    • 84990719446 scopus 로고
    • Some applications of nonlinear convergence accelerators
    • Homeier, H. H. H.: Some applications of nonlinear convergence accelerators, Internat. J. Quantum Chem. 45 (1993), 545-562.
    • (1993) Internat. J. Quantum Chem. , vol.45 , pp. 545-562
    • Homeier, H.H.H.1
  • 9
    • 0001873635 scopus 로고
    • A hierarchically consistent, iterative sequence transformation
    • Homeier, H. H. H.: A hierarchically consistent, iterative sequence transformation, Numer. Algorithms 8 (1994), 47-81.
    • (1994) Numer. Algorithms , vol.8 , pp. 47-81
    • Homeier, H.H.H.1
  • 10
    • 50749136181 scopus 로고
    • Determinantal representations for the ℐ transformation
    • Homeier, H. H. H.: Determinantal representations for the ℐ transformation, Numer. Math. 71(3) (1995), 275-288.
    • (1995) Numer. Math. , vol.71 , Issue.3 , pp. 275-288
    • Homeier, H.H.H.1
  • 11
    • 0030120858 scopus 로고    scopus 로고
    • Analytical and numerical studies of the convergence behavior of the ℐ transformation
    • Homeier, H. H. H.: Analytical and numerical studies of the convergence behavior of the ℐ transformation, J. Comput. Appl. Math. 69 (1996), 81-112.
    • (1996) J. Comput. Appl. Math. , vol.69 , pp. 81-112
    • Homeier, H.H.H.1
  • 12
    • 0041539298 scopus 로고    scopus 로고
    • Correlation energy estimators based on Møller-Plesset perturbation theory
    • Homeier, H. H. H.: Correlation energy estimators based on Møller-Plesset perturbation theory, J. Molec. Struct. (Theochem) 366 (1996), 161-171.
    • (1996) J. Molec. Struct. (Theochem) , vol.366 , pp. 161-171
    • Homeier, H.H.H.1
  • 14
    • 0004705637 scopus 로고    scopus 로고
    • The size-extensivity of correlation energy estimators based on effective characteristic polynomials
    • Proc. 3rd Electronic Computational Chemistry Conf.
    • Homeier, H. H. H.: The size-extensivity of correlation energy estimators based on effective characteristic polynomials, J. Molec. Struct. (Theochem) 419 (1997), 29-31. Proc. 3rd Electronic Computational Chemistry Conf.
    • (1997) J. Molec. Struct. (Theochem) , vol.419 , pp. 29-31
    • Homeier, H.H.H.1
  • 15
    • 0041725604 scopus 로고    scopus 로고
    • On the stability of the ℐ transformation
    • Homeier, H. H. H.: On the stability of the ℐ transformation, Numer. Algorithms 17 (1998), 223-239.
    • (1998) Numer. Algorithms , vol.17 , pp. 223-239
    • Homeier, H.H.H.1
  • 16
    • 0029408759 scopus 로고
    • On remainder estimates for Levin-type sequence transformations
    • Homeier, H. H. H. and Weniger, E. J.: On remainder estimates for Levin-type sequence transformations, Comput. Phys. Comm. 92 (1995), 1-10.
    • (1995) Comput. Phys. Comm. , vol.92 , pp. 1-10
    • Homeier, H.H.H.1    Weniger, E.J.2
  • 19
    • 0001711117 scopus 로고    scopus 로고
    • A new iterative method for solving the time-independent Schrödinger equation based on the generalized Bloch equation. I. Boson systems: The quartic anharmonic oscillator
    • Meißner, H. and Steinborn, E. O.: A new iterative method for solving the time-independent Schrödinger equation based on the generalized Bloch equation. I. Boson systems: The quartic anharmonic oscillator, Internat. J. Quantum Chem. 61 (1997), 777-795.
    • (1997) Internat. J. Quantum Chem. , vol.61 , pp. 777-795
    • Meißner, H.1    Steinborn, E.O.2
  • 20
    • 5344271877 scopus 로고    scopus 로고
    • Quartic, sextic, and octic anharmonic oscillators: Precise energies of ground state and excited states by an iterative method based on the generalized Bloch equation
    • Meissner, H. and Steinborn, E. O.: Quartic, sextic, and octic anharmonic oscillators: Precise energies of ground state and excited states by an iterative method based on the generalized Bloch equation, Phys. Rev. A 56 (1997), 1189-1200.
    • (1997) Phys. Rev. a , vol.56 , pp. 1189-1200
    • Meissner, H.1    Steinborn, E.O.2
  • 21
    • 0032495961 scopus 로고    scopus 로고
    • Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: Application to anharmonic oscillators
    • Sergeev, A. V. and 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.
    • (1998) J. Phys. A: Math. Gen. , vol.31 , pp. 4301-4317
    • Sergeev, A.V.1    Goodson, D.Z.2
  • 22
    • 0016047525 scopus 로고
    • On quadratic approximation
    • Shafer, R. E.: On quadratic approximation, SIAM J. Numer. Anal. 11 (1974), 447-460.
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 447-460
    • Shafer, R.E.1
  • 23
    • 85171863190 scopus 로고
    • Non-linear transformations of divergent and slowly convergent sequences
    • Shanks, D.: Non-linear transformations of divergent and slowly convergent sequences, J. Math. and Phys. 34 (1955), 1-42.
    • (1955) J. Math. and Phys. , vol.34 , pp. 1-42
    • Shanks, D.1
  • 24
    • 0039675005 scopus 로고
    • Coupling constant analyticity for the anharmonic oscillator
    • Simon, B.: Coupling constant analyticity for the anharmonic oscillator, Ann. Phys. (NY) 58 (1970), 76-136.
    • (1970) Ann. Phys. (NY) , vol.58 , pp. 76-136
    • Simon, B.1
  • 25
    • 0001626745 scopus 로고
    • The anharmonic oscillator: A singular perturbation theory
    • D. Bessis (ed.), Gordon and Breach, New York
    • Simon, B.: The anharmonic oscillator: A singular perturbation theory, In: D. Bessis (ed.), Cargèse Lectures in Physics, Vol. 5, Gordon and Breach, New York, 1972, pp. 383-414.
    • (1972) Cargèse Lectures in Physics , vol.5 , pp. 383-414
    • Simon, B.1
  • 26
    • 0003105647 scopus 로고
    • Acceleration of linear and logarithmic convergence
    • Smith, D. A. and Ford, W. F.: Acceleration of linear and logarithmic convergence, SIAM J. Numer. Anal. 16 (1979), 223-240.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 223-240
    • Smith, D.A.1    Ford, W.F.2
  • 28
    • 0343863901 scopus 로고
    • Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series
    • Weniger, E. J.: Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Phys. Rep. 10 (1989), 189-371.
    • (1989) Comput. Phys. Rep. , vol.10 , pp. 189-371
    • Weniger, E.J.1
  • 30
    • 34848924872 scopus 로고
    • The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic and octic anharmonic oscillators using nonlinear sequence transformations
    • Weniger, E. J., Čížek, J. and Vinette, F.: The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic and octic anharmonic oscillators using nonlinear sequence transformations, J. Math. Phys. 34 (1993), 571-609.
    • (1993) J. Math. Phys. , vol.34 , pp. 571-609
    • Weniger, E.J.1    Čížek, J.2    Vinette, F.3
  • 32
    • 0038653642 scopus 로고
    • The three-point Padé resummation of perturbation series for anharmonic oscillators
    • Znojil, M.: The three-point Padé resummation of perturbation series for anharmonic oscillators, Phys. Lett. A 177 (1993), 111-120.
    • (1993) Phys. Lett. A , vol.177 , pp. 111-120
    • Znojil, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.