Abstract
Whenever a discriminant function is constructed, the attention of a researcher is often focused on classification. The underlined interest is how well does a discriminant function perform in classifying future observations correctly. In order to assess the performance of any classification rule, probabilities of misclassification of a discriminant function serves as a basis for the procedure. Different forms of probabilities of misclassification and their associated properties were considered in this study. The misclassification probabilities were defined in terms of probability density functions (pdf) and classification regions. Apparent probability of misclassification is expressed as the proportion of observations in the initial sample which are misclassified by the sample discriminant function. Different methods of estimating probabilities of misclassification were related to each other using their individual shortcomings. The status of degrees of uncertainties associated with probabilities of misclassification and their implications were also specified.
Highlights
In mathematical modeling of various physical phenomena, initial and boundary-value problems arise for differential equations with small parameters at higher derivatives [1].Due to the importance of such problems, the construction of various schemes of the convective-diffusion problem is the subject of the work of many authors [2,3,4,5,6,7,8,9,10,11,12,13,14]
To improve the quality of difference schemes, the method of moving nodes is used in combination with Richardson interpolation
The construction of discrete analogues of the convective-diffusion equation plays an essential role for transport processes
Summary
In mathematical modeling of various physical phenomena, initial and boundary-value problems arise for differential equations with small parameters at higher derivatives [1]. The construction of discrete analogues of the convective-diffusion equation plays an essential role for transport processes This is especially true when discrete analogues of the Navier-Stokes equation are constructed for large Reynolds numbers. In this regard, the movable nodes method (MNM) allows in many cases to design higher-quality discrete analogs of differential equations. MMN for simple cases allows you to get an analytical representation of the solution between the nodal points of the boundary value problem. Based on this representation, it is possible to construct a higher-quality discrete scheme.
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