2024 , Volume 29, № 2, p.35-61

The paper addresses methods for the solution of curve ҥtting problem from inaccurate data that have interval uncertainty, i. e. about which it is only known that they belong to some intervals of possible values. Under these conditions, it is necessary to construct a functional dependence from a given class that has the best possible consistency (compatibility) with the interval data. In order to construct the required functional dependence, we develop the maximum compatibility method, in which, to ҥnd the parameters of a function, it is required to maximize the so-called recognizing functional of the solution set to an interval system of equations built from interval data and the expression of the constructed function. A strong version of the maximum compatibility method is preferred, as it is more practical and has better theoretical properties. Previously, a strong version of the maximum compatibility method has successfully proven itself in solving data ҥtting for linear function, from interval data.

In the theoretical part of the paper, a general approach to the nonlinear curve ҥtting problem is proposed, and then the practically important fractional-linear function is discussed in more detail. It is shown that the recognizing functional of the information set of the problem in this special case is a quasi-concave function, so that its maximum is unique. In addition, the quasi-concavity property radically simpliҥes the numerical maximization of the recognizing functional. As a practical application, the problem of processing interval measurement data of the electrochemical process of metal deposit formation is solved.

Finally, the paper considers a generalization of the proposed technique for constructing the best ҥt linear-fractional functions from interval data applied to the case of an arbitrary number of variables. We substantiate the quasi-concavity of the recognizing functional of the information set for the problem arising in this case, which allows applying the developed methods of non-smooth optimization for ҥnding their maximums