Regularized Newton type method for retrieval of heavy water in atmosphere by IR–spectra of the solar light transmission

The inverse problem of reconstructing the vertical profiles of HDO/H$_2$O in the atmosphere by IR-spectra of solar light transmission is investigated. For solving this problem the two-stage method is suggested. On the first stage, we apply the Tikhonov regularization method with a special stabilizer. On the second stage, to approximate a solution of the regularized equation, we use a Fejér process of Newton-type. The convergence theorems are formulated, the Fejér property of iterations is substantiated and the results of numerical experiments for series of measured spectra are presented.