Ellipsoidal Approximation of the Set of Solutions of Interval Systems of Linear Algebraic Equations

Abstract

The article presents the results of the approximation of the set of solutions of interval systems of linear algebraic equations. These systems are used in the problems of modeling linear deterministic processes. It is assumed that the modeled process is described by an output variable and a set of input variables, the measurement errors of which are assumed to be set by known intervals symmetric with respect to the zero value. Traditionally, the sets of solutions of interval systems of linear algebraic equations in applied problems are approximated by a hyper-rectangular whose sides are parallel to the axes of the selected coordinate system. In this paper, we propose to use an ellipsoidal approximation of these sets, which is more efficient. The main results of the work include the substantiation of assumptions about the properties of the modeled process, the choice of a mathematical method for constructing an approximating ellipsoid, the proposed method for forming boundary points, and a numerical method for solving the problem. A computer simulation of the problem of estimating the parameters of a linear process is performed in Excel, which is used for a comparative study of approximations of solutions of interval systems of linear algebraic equations by a hyper-rectangular and an ellipse.