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- Giorgini, Ludovico Theo, et al.
(author)
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Correlation functions of the anharmonic oscillator : Numerical verification of two-loop corrections to the large-order behavior
- 2022
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In: Physical Review D. - : American Physical Society (APS). - 2470-0010 .- 2470-0029. ; 105:10
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Journal article (peer-reviewed)abstract
- Recently, the large-order behavior of correlation functions of the O(N)-anharmonic oscillator has been analyzed by us [L. T. Giorgini et al., Phys. Rev. D 101, 125001 (2020)]. Two-loop corrections about the instanton configurations were obtained for the partition function, the two-point and four-point functions, and the derivative of the two-point function at zero momentum transfer. Here, we attempt to verify the obtained analytic results against numerical calculations of higher-order coefficients for the O(1), O(2), and O(3) oscillators, and we demonstrate the drastic improvement of the agreement of the large-order asymptotic estimates and perturbation theory upon the inclusion of the two-loop corrections to the large-order behavior.
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| 2. |
- Jentschura, Ulrich D., et al.
(author)
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Enhanced and generalized one–step Neville algorithm : Fractional powers and access to the convergence rate
- 2024
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In: Computer Physics Communications. - : Elsevier BV. - 0010-4655 .- 1879-2944. ; 303
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Journal article (peer-reviewed)abstract
- The recursive Neville algorithm allows one to calculate interpolating functions recursively. Upon a judicious choice of the abscissas used for the interpolation (and extrapolation), this algorithm leads to a method for convergence acceleration. For example, one can use the Neville algorithm in order to successively eliminate inverse powers of the upper limit of the summation from the partial sums of a given, slowly convergent input series. Here, we show that, for a particular choice of the abscissas used for the extrapolation, one can replace the recursive Neville scheme by a simple one-step transformation, while also obtaining access to subleading terms for the transformed series after convergence acceleration. The matrix-based, unified formulas allow one to estimate the rate of convergence of the partial sums of the input series to their limit. In particular, Bethe logarithms for hydrogen are calculated to 100 decimal digits. Generalizations of the method to series whose remainder terms can be expanded in terms of inverse factorial series, or series with half-integer powers, are also discussed.
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