Unstable solutions in digitization of experimental data in experimental plasma physics

Many problems in science and engineering can be formulated as linear inverse problems, i.e., the problems that require determination of the unknown input (the model parameters) to a linear system from the known output (the experimental data). Computer-supported techniques play an important role in the evaluation of experimental data but digitalization of inverse problems generally gives rise to very ill-conditioned linear system of algebraic equations. Most of these problems are ill-posed (too sensitive on experimental error). Usually, the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible. This means that the systems must be replaced with nearby systems that are less sensitive to perturbations. In this work Tikhonov regularization method was used, as an effective way to transfer an ill-posed problem to a correct one (less sensitive to perturbations). The regularization FORTRAN subroutine has been adapted for different experimental applications in problems of plasma diagnostic. The model functions have been introduced to check applicability limitations of the method. Reasonable recovering of unknown functions from experimental data was found.