Statistics – Computation
Scientific paper
Dec 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phrva..56.5165w&link_type=abstract
Physical Review A (Atomic, Molecular, and Optical Physics), Volume 56, Issue 6, December 1997, pp.5165-5168
Statistics
Computation
19
Quantum Mechanics, Sequences, Series, And Summability, Computational Techniques, Simulations
Scientific paper
The performance of the so-called superconvergent perturbation theory [W. Scherer, Phys. Rev. Lett. 74, 1495 (1995)] is investigated numerically in the case of the ground-state energy of a quartic anharmonic oscillator. It is shown that Scherer's superconvergent approximation, which is rational in the coupling constant β, gives in the case of small coupling constants somewhat better results than the strongly divergent but asymptotic Rayleigh-Schrödinger perturbation series if it is truncated at the same order in β. However, the transformation of this truncated perturbation series into Padé approximants or into another class of rational functions by means of the sequence transformation δ(n)k(ζ,sn) [E. J. Weniger, Comput. Phys. Rep. 10, 189 (1989)] yields much more powerful rational approximants. Moreover, the performance of the superconvergent approximation can be improved considerably by Wynn's epsilon algorithm [P. Wynn, Math. Tables Aids Comput. 10, 91 (1956)] or by δ(n)k(ζ,sn). Finally, it is shown that the other rational approximants provide much better approximations to higher order terms of the Rayleigh-Schrödinger perturbation series than Scherer's superconvergent approximation.
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