scholarly journals Improved Algorithm for Determining of "Saturated Block" in the Task of Parametric Identification Interval System of Linear Algebraic Equations

2016 ◽  
Vol 26 (5) ◽  
pp. 345-363
Author(s):  
I.S. Oliynyk
Keyword(s):  
Parametric Identification ◽  
Algebraic Equations ◽  
Interval System ◽  
Linear Algebraic Equations ◽  
Improved Algorithm

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.

scholarly journals RESEARCH OF OBJECTIVE FUNCTION IN PARAMETRIC IDENTIFICATION TASKS FOR INTERVAL DIFFERENCE OPERATOR WITH REQUIRED ACCURACY

2011 ◽  
pp. 162-171
Author(s):  
Mykola Dyvak ◽  
Taras Dyvak ◽  
Petro Stakhiv
Keyword(s):  
Objective Function ◽  
Difference Operator ◽  
Random Search ◽  
Parametric Identification ◽  
Interval Data ◽  
Algebraic Equations ◽  
Criterion Function ◽  
Interval System ◽  
Nonlinear Algebraic Equations

The paper presents the problems of parametric identification of nonlinear difference operator based on interval data. It is showed that, formally, this problem belongs to the task of finding at least of one solution of interval system of nonlinear algebraic equations. It is proposed and justified the use of the methods of random search with a nonlinear discrete criterion function for solving this task. The properties of the function are researched in this paper.

New improved algorithm for the iterative solution of a system of linear algebraic equations

1982 ◽  
Vol 27 (1) ◽  
pp. 87-89 ◽  
Author(s):  
L.L. Kosachevskaya ◽  
V.V. Romanovtsev ◽  
I.E. Shparlinskiy ◽  
A.N. Vystavkin
Keyword(s):  
Iterative Solution ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Improved Algorithm

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.

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