Abstract
Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). The relationships among the classification statistics examined were established: The Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification statistics.
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.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call