scholarly journals Estimation Method for a Set of Solutions to Interval System of Linear Algebraic Equations with Optimized “Saturated Block” Selection Procedure

2017 ◽  
Vol 7 (1) ◽  
pp. 17-24 ◽  
Author(s):  
Mykola Dyvak ◽  
◽  
Iryna Oliynyk ◽  
Keyword(s):  
Estimation Method ◽  
Selection Procedure ◽  
Algebraic Equations ◽  
Interval System ◽  
Linear Algebraic Equations

scholarly journals CONSTRUCTION OF EXPERT-STATISTICAL MODELS FROM INCOMPLETE DATA

T-Comm ◽  
2021 ◽  
Vol 15 (6) ◽  
pp. 33-39
Author(s):  
Sergey I. Noskov ◽  
Keyword(s):  
Linear Regression ◽  
Statistical Models ◽  
Incomplete Data ◽  
Algebraic Equations ◽  
Linear Regression Equation ◽  
Railway Transport ◽  
Specific Question ◽  
Interval System ◽  
Linear Algebraic Equations ◽  
Initial Uncertainty

The article deals with the problem of constructing a linear regression model based on incomplete data containing gaps, using statistical and expert information. The reasons for the gaps in the data can be, in particular, a temporary malfunction (failure) of the measuring equipment when taking various technical characteristics, or negligence in the work of statistical services when fixing the reporting indicators. Very often, gaps arise when processing various kinds of sociological information in the form of questionnaires, when respondents refuse to answer a specific question (but answer others) or give an inadmissible, in particular, evasive answer. The approach proposed in the work involves filling the gaps with intervals, the boundaries of which are formed by experts, guided by both their experience and knowledge about the object of research, and using the well-known methods of point filling in the gaps. After that, the estimation of the parameters of the model, depending on the nature of the initial uncertainty in the data, is reduced to solving problems of linear or partially Boolean linear programming. The case is considered when the solution of the formalizing uncertainty in the initial data of the interval system of linear algebraic equations is not unique. The problem of constructing a linear regression equation for the influence of the volume of export of large-tonnage containers and the freight turnover of the PRC railway transport on the volume of import of large-capacity containers at the Zabaikalsk-Manchuria railway checkpoint is solved.

A shifted Legendre method for solving a population model and delay linear Volterra integro-differential equations

2017 ◽  
Vol 10 (07) ◽  
pp. 1750091 ◽  
Author(s):  
Şuayip Yüzbaşi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Matrix Equation ◽  
Population Model ◽  
Estimation Method ◽  
Approximate Solutions ◽  
Algebraic Equations ◽  
Integro Differential Equation ◽  
Linear Algebraic Equations ◽  
The Matrix

In this paper, we propose a collocation method to obtain the approximate solutions of a population model and the delay linear Volterra integro-differential equations. The method is based on the shifted Legendre polynomials. By using the required matrix operations and collocation points, the delay linear Fredholm integro-differential equation is transformed into a matrix equation. The matrix equation corresponds to a system of linear algebraic equations. Also, an error estimation method for method and improvement of solutions is presented by using the residual function. Applications of population model and general delay integro-differential equation are given. The obtained results are compared with the known results.

Combined method for correction interval systems of linear algebraic equations

Metrologiya ◽  
2021 ◽  
pp. 17-39
Author(s):  
A. N. Bazhenov ◽  
A. Yu. Telnova
Keyword(s):  
Linear Equations ◽  
Interval Uncertainty ◽  
Algebraic Equations ◽  
System Matrix ◽  
Combined Method ◽  
Interval System ◽  
Linear Algebraic Equations ◽  
Linear Interval ◽  
Systems Of Linear Equations ◽  
Interval Systems

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.

scholarly journals PC-solutions and quasi-solutions of the interval system of linear algebraic equations

2021 ◽  
Vol 17 (3) ◽  
pp. 262-276
Author(s):  
Sergei I. Noskov ◽  
◽  
Anatoly V. Lakeyev ◽  
Keyword(s):  
Interval Analysis ◽  
Linear Inequalities ◽  
Algebraic Equations ◽  
System Of Linear Inequalities ◽  
Interval System ◽  
Linear Algebraic Equations ◽  
System Of Inequalities ◽  
Nonlinear Condition ◽  
Left And Right ◽  
Intensive Development

The problem of solving the interval system of linear algebraic equations (ISLAEs) is one of the well-known problems of interval analysis, which is currently undergoing intensive development. In general, this solution represents a set, which may be given differently, de- pending on which quantifiers are related to the elements of the left and right sides of this system. Each set of solutions of ISLAE to be determined is described by the domain of compatibility of the corresponding system of linear inequalities and, normally, one nonlinear condition of the type of complementarity. It is difficult to work with them when solving specific problems. Therefore, in the case of nonemptiness in the process of solving the problem it is recommended to find a so-called PC-solution, based on the application of the technique known in the theory of multi-criterial choice, that presumes maximization of the solving capacity of the system of inequalities. If this set is empty, it is recommended to find a quasi- solution of ISLAE. The authors compare the approach proposed for finding PC- and/or quasi-solutions to the approach proposed by S. P. Shary, which is based on the application of the recognizing functional.

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