A theoretical evaluation of a method of solving ill-conditioned inverse problems that arise in mathematicostatistical processing of measurement information under conditions of unavoidable errors in measurements and a mathematical model of the study object is considered. The method is based on physical and canonical decomposition of the initial model of the object, specified in the form of a system of linear equations as well as two-sided regularization of the solution of a canonical (diagonal) system of equations. It is shown that through the use of the method it is possible to create an adaptive algorithm for recognition and stable estimation of a group of information parameters of a physically decomposed model.
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07 August 2018
Formula (20) and (21) has been corrected. Also, on page 230, in the 7th line of the conclusion, it should read “estimated parameters of the decomposed model (9);”.
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Translated from Metrologiya, No. 1, pp. 17–35, January–March, 2018.
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Surnin, Y.V. Decomposition and Regularization of the Solution of Ill-Conditioned Inverse Problems in Processing of Measurement Information. Part 1. A Theoretical Evalution of the Method. Meas Tech 61, 223–231 (2018). https://doi.org/10.1007/s11018-018-1413-6
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DOI: https://doi.org/10.1007/s11018-018-1413-6