DOI: 10.17587/prin.7.181-190

Unification of Point Algebraic Techniques of an Exterior Estimation of Set Solutions Interval Systems

K. F. Ivanova, e-mail: Klara.I2010@yandex.ru, Saint-Petersburg State University, 195252, Saint Petersburg, Russian Federation

Corresponding author: Ivanova Klara F., Doctorant, Saint-Petersburg State University, 195252, Saint Petersburg, Russian Federation e-mail: Klara.I2010@yandex.ru

In the work a unified technique of exterior estimating the solution sets of interval systems of the linear algebraic equations (ISLAE) with uncertain parameters in both narrow and wide interval ranges of modification of elements for systems with M-and H-matrices and to their modifications is offered. The offered technique of estimation is based on choice of point elements of an interval matrix and of a component of right-hand side vector entering into componentwise products of elements of an interval matrix on their algebraic deviations. This choice is carried out based on extremalizating the received scalar product by identifying the point value of an element of the new matrix with one of the corresponding boundary values of an element of an interval matrix and a point right-hand side new vector with boundary of a corresponding component of an interval right-hand side vector. As a result of the performed operation for choosing minimal and universal elements and the component is formed by two point matrices and two point vectors from which it is possible to generate two systems consisting of four point linear algebraic equations. The formalized point matrices ensure the minimal and maximal values of the determinants, similar to two boundaries of an interval determinant of an initial matrix. The solution of the obtained point set of equations there are double-dimension vectors х that have the minimal and maximal deviations as their components.

Keywords: interval system, uncertainty of parameters, extremalization, a scalar product, the formalized matrixes, a technique of estimate, set solutions, an exterior estimation, the point equations

pp. 181–190

For citation:
Ivanova K. F. Unification of Point Algebraic Techniques of an Exterior Estimation of Set Solutions Interval Systems, Programmnaya Ingeneria, 2016, vol. 7, no. 4, pp. 181—190.

This work was supported by research works on theme NIR "The structural fundamental focused modelling of polytechnical nanostructures" under the state contract № 9.0.112.2009.