Conclusion
The method presented above for constructing rational approximants and obtaining their statistical characteristics is fairly convenient and universal. When it is considered that exponential-harmonic analysis also reduces to rational approximation, not of the function itself but of the application of the Fourier and Laplace transforms to the function [15a, b], the range of application of this method encompasses practically all the major systems of approximating functions. The existence of pole singularities in the Padé approximant is an extremely valuable analytic property, substantially expanding the region of convergence and increasing its speed as compared with the polynomial approximation. The Padé approximation is particularly a natural instrument for processing resonance curves since the resonances correspond to complex poles of the approximant. But in the general case as well analytic representation of data in this form is convenient and compact. Thus, representation of data on the cross sections for threshold reactions under the action of neutrons (BOSPOR library [14h]) in the form of rational functions resulted in a 20-fold reduction of the numerical information subject to storage as compared with the pint-by-point assignment with the same accuracy of description. All of this enables the Padé approximation to be considered as a promising method of representing neutron and nuclear data.
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Translated from Atomnaya Énergiya, Vol. 56, No. 1, pp. 20–25, January, 1984.
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Badikov, S.A., Vinogradov, V.A., Gai, E.V. et al. Analytic approximation of neutron physics data. At Energy 56, 19–26 (1984). https://doi.org/10.1007/BF01123607
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DOI: https://doi.org/10.1007/BF01123607