General problems of regularizability

Any mathematical model sets some correspondence between two kinds of objects. One class of objects includes characteristics of the model, and the other consists of experimentally observed attributes of the studied phenomena. The problems of processing experimental data are always concerned with inevitable experimental errors. For the purposes of present analysis, we shall consider the objects of the second kind belonging to some metric space X, and of the first kind - to space Y. The mathematical model establishes the certain correspondence y =G(x) between input datax∈Xand characteristics of the model y∈ Y. Modeling is aimed at obtaining model characteristics y using approximately specified input datax.