Asymptotically exact method for calculation of density of states in HTSC

The work presents the method of restoring a spectral density from known Green's function. The method is based on a combination of Monte Carlo and gradient descent algorithms, which avoids the problem of distortion of the equation by nonlinear terms and, therefore, analyzes the most representative range of small deviations. Furthermore, the method does not contain sources of systematic errors and, in principle, any spectral function can be parameterized with any desired accuracy. With the use of the method, the spectral density of states was restored for FeAs-based superconductors. The method works well also for metal nanoclusters and many other systems.