Andriy L. Development of mathematical methods and algorithms for decision of super-resolution measuring-calculating systems modeling problems

The dissertation is dedicated to development of methods for super-resolution measuring-calculating systems modeling problems solving. Linear operator equations of first kind is used as measurements model. The new methods for pareto-optimum estimation of the given device's output by noised output of other device on the same input are developed in various cases. Specifically, the estimations are obtained for the cases: gradual and simultaneous receipt of measurements' results; unknown measurements process' model; unstable statistical characteristics of experimental data's errors; additional restrictions for measuring process specified by matrix of a special kind. The constructed methods are based on ideas of pareto-optimization, abstract function differentiation, spline approximation and uses possibility-theoretic and probability-theoretic approaches' features. The research of the received estimations and their comparison with already existing estimations is done. The important and actual applied problems of measurements' reduction to calculations are solved.