Interval Methods for Data Fitting Under Imprecision and Uncertainty

Abstract

We consider the data fitting problem under interval uncertainty and show that the problem reduces to the solution of interval systems of equations constructed from the data being processed. The paper discusses in detail the so-called strong compatibility of parameters and data, as more practical, more adequate to reality and possessing better theoretical properties. Estimates of function parameters that satisfy the strong compatibility conditions have polynomial computational complexity, are robust, and almost always have finite variability. The paper proposes a computational technology for solving the data fitting problem for linear function, under interval data uncertainty and taking into account the requirement of strong compatibility.