Application of Interval Approach to Spectral Analysis. Investigation of Solvability of a Problem with the Use of a Recognizing Functional

Abstract

The application of interval analysis in a linear formulation (linear problem of tolerances) to a concrete problem of spectral analysis is considered. The principal procedural objective is to demonstrate the use of a recognizing functional as an investigatory tool. The method of intervalization of the right sides of an interval system of linear algebraic equations without recourse to models of the form of the background under a peak along with the form of united solution sets of an interval system of linear algebraic equations for a particular problem are studied. The solvability of an interval system of linear algebraic equations relative to the sign of the recognizing functional is investigated, and it is shown that in the initial formulation the system is not solvable. Methods of attaining solvability by weakening the tolerances of the right side of the system and through a modification of the matrix are considered and results of the use of both methods are discussed.