Stochastic Properties of the SVD Decomposition. Identification of Distribution Densities for Singular Values of Matrix Operators in Solving Slae
It is suggested to study stochastic properties of matrix operators and the classical SVD decomposition by methods of the identification of distribution densities for singular values. The need for research is determined by the influence of probabilistic characteristics of the singular decomposition on finding normal SLAE pseudo-solutions. The approach under development is also effective when analyzing time series within the SSA-method. The suggested method is based on solving the Fredholm integral equation of the first kind using a limited sampling of perturbed singular values. The identification of singular value distributions is methodologically and programmatically worked out on simulated and real experimental data. In this paper we consider examples with significant variations in characteristic structures of matrices responsible for the stability of solutions.