Inverse problems of vibrational spectroscopy as nonlinear ill-posed problems (Q1286803)

This study, based on previous works of the authors, makes an attempts to describe the main mathematical results necessary for data processing in vibrational spectroscopy. On the basis of a formalization of the model assumptions, in the framework of Tikhonov's regularization theory, the authors have constructed a principle for choosing a unique solution from the set of solutions. Such a principle has been formulated in terms of the closeness of the solution to the given matrix of force constants which satisfy all a priori assumptions concerning the model characteristics of the solution. In addition to theoretical considerations and based on Tikhonov's regularization method, they also investigated stable numerical methods for computing the force fields of polyatomic molecules from experimental data and provided some numerical illustrations with real data. The proposed algorithms have been implemented using software package spectrum.