Combined method for correction interval systems of linear algebraic equations

Abstract

The possibility of application of the interval analysis for data processing in the field of spectral analysis is considered. It is assumed that the data have interval uncertainty; therefore the problem of finding unknown concentrations is posed as a linear interval tolerance problem. The incompatibility of the interval system of linear algebraic equations is shown for the initial data using the apparatus of the recognizing functional. The relevance of the topic is due to the need for regularization of inconsistent interval systems of linear equations. The idea of S. P. Shary of a combined method for correcting a linear tolerance problem has been implemented. A new method for managing the solution by changing the linear algebraic equations interval system matrix elements radii has been developed. The research results can be used for example, to calculate the substance’s concentrations by measurement of the characteristic X-ray radiation.