Curve Fitting for Exponential Polynomials from Interval Data

The article is devoted to solving the curve fitting problem for exponential polynomials from interval data. The goal of the work is to describe, implement and test the algorithm of curve fitting for exponential polynomials. The curve fitting algorithm is a generalization of the Maximal Compatibility Method for a given class of functions. The key idea is to implement a measure of data compatibility and to find the maximum of this measure. Thus, the problem of curve fitting boils down to the problem of a non-smooth non-concave conditional maximization of a function called recognizing functional. Subgradient methods, the penalty function method and multistart technology were used to solve this problem. In the course of the work, an explicit form of optimization problem was built, a software implementation was made, several examples demonstrating the performance of technology were built. The results of the work can be used in applied research to solve the problem of curve fitting, where the uncertainty of the data can be described with the help of intervals and the guaranteed nature of the estimates is required.