Stochastic algorithms for solving linear and nonlinear inverse ill-posed problems for particle size retrieving and x-ray diffraction analysis of epitaxial films

We suggest stochastic simulation techniques for solving two classes of linear and nonlinear inverse and ill-posed problems: (1) recovering the particle nanosize distribution from diffusion battery measurements, (2) retrieving the step structure of the epitaxial films from the x-ray diffraction analysis. To solve these problems we develop three stochastic based methods: (1) the random projection method, a stochastic version of the Kaczmarz method, (2) a randomized SVD method, (3) stochastic genetic algorithm. Results of comparative simulations of the three methods are also presented.