Geodesic
A method for estimating the statistical error of the solution in the inverse spectroscopy problem
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 58 (2021), pp. 3-17

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A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.
Mots-clés : solution error interval
Keywords: inverse problem, normal distribution law, Mössbauer spectroscopy, mean squared error, partial components. 
@article{IIMI_2021_58_a0,
     author = {T. M. Bannikova and V. M. Nemtsov and N. A. Baranova and G. N. Konygin and O. M. Nemtsova},
     title = {A method for estimating the statistical error of the solution in the inverse spectroscopy problem},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {3--17},
     publisher = {mathdoc},
     volume = {58},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2021_58_a0/}
}
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T. M. Bannikova; V. M. Nemtsov; N. A. Baranova; G. N. Konygin; O. M. Nemtsova. A method for estimating the statistical error of the solution in the inverse spectroscopy problem. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 58 (2021), pp. 3-17. http://geodesic.mathdoc.fr/item/IIMI_2021_58_a0/