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Almost complete convergence for the sequence of approximate solutions in linear calibration problem with \(\alpha\)-mixing random data. (English) Zbl 1498.47030

Summary: In this work, we propose a stochastic method which gives an estimated solution for a linear calibration problem with \(\alpha\)-mixing random data. We establish exponential inequalities of Fuk-Nagaev type, for the probability of the distance between the approximate solutions and the exact one. Furthermore, we build a confidence domain for the so mentioned exact solution. To check the validity of our results, a numerical example is proposed.

MSC:

47A52 Linear operators and ill-posed problems, regularization
53C38 Calibrations and calibrated geometries
62L20 Stochastic approximation
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