The condition number of a matrix as an optimality criterion in the problems of parametric identification of linear equations systems

Abstract

When solving applied problems, an important aspect of the analysis is the stability of the obtained solution with respect to experimental data errors. Empirical experimental data, although a priori inaccurate, can be represented by intervals of their range of values. In some cases, the limits of their variation may also be known. Obviously, the degree of inaccuracy of input data influences the solution of the parametric identification problem. Therefore, in the case when this solution is not the only one, methods for assessing the influence of experimental error on the stability of each potential solution are of interest as they may provide additional arguments in favour of choosing one of them. In the case of models formalized in the form of systems of linear algebraic equations, a similar effect can be investigated using the condition number. In a case of quantitative analysis of multicomponent mixtures, the paper presents an approach to the parametric identification of linear models based on the calculation of the maximum permissible parameter estimates in combination with the study of the coefficient stability of the system.