NEW TOOLS OF CYBERNETICS, INFORMATICS, COMPUTER ENGINEERING, AND SYSTEMS ANALYSIS: MODEL SELECTION CRITERIA FOR A LINEAR MODEL TO SOLVE DISCRETE ILL-POSED PROBLEMS ON THE BASIS OF SINGULAR DECOMPOSITION AND RANDOM PROJECTION

摘要

Criteria are developed to determine the optimal number of components of a linear model in solving a discrete ill-posed problem by the methods of truncated singular value decomposition and random projection. To this end, the behavior of dependencies of the error vector of the solution and the restoration error of the vector of the right side on the model dimensionality and their minima is investigated. An experimental investigation of the developed criteria was also pursued and its results are provided.