Article 2218

Title of the article

HARMONIC APPROXIMATION AND PIECEWISE-RULED LAGRANGE INTERPOLATION OF FUNCTIONS OF SEVERAL VARIABLES
AS APPLIED TO AIRCRAFT EQUIPMENT 

Authors

Lapshin Eduard Vladimirovich, doctor of technical sciences, professor, sub-department of radio equipment design and production, Penza State University (440026, 40 Krasnaya street, Penza, Russia), edlapshin@mail.ru

Index UDK

629.7.072.8

DOI

10.21685/2307-4205-2018-2-2

Abstract

Modular technical training once again raises the question of problem oriented computing methods for computerization and training simulators. This could include options for methods outlined in this article. A new method for fast piecewise-linear interpolation to low uniform or non-uniform grid is focused on functions of many variables (up to 8–10). Its shortcomings are more than repaid computational efficiency, creating the ability to imitate important effects, particularly in critical flight modes. Method for solving multiextreme multidimensional tasks enables you to quickly implement complex parametric optimization. Some promotion achieved objectives synthesis of models of physical factors. For modeling tasks in technical means of teaching the accuracy of source arrays of data usually is low (errors are calculated per cent). The main advantage of the harmonic (spectral) represent an expression of the approximating function is the possibility of formalized analysis image (topology) function from the perspective of the necessary detail descriptions. Such formal analysis is required for the use of other more convenient methods of approximation (including piecewise linear interpolation method on sparse grid). When this maximum error of piecewise linear interpolation can be units per cent. Further justification for such rules specify the grid will be given discretion with respect to the piecewise-bar and piecewise linear interpolation functions of many arguments. Note that the trigonometric model of approximation function has another positive quality. In view of the orthogonal basis functions it is useful for the identification process. With the appropriate information technology of identification of coefficients of harmonics are determined not by the equations, and directly in the course of receiving and processing of experimental data.

Key words

aviation simulators, simulators and mathematical models of objects, piecewise-linear interpolation, methods and means of identification method of approximation

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Дата создания: 18.06.2018 14:05
Дата обновления: 18.06.2018 15:21