THE ALGORITHM FOR DETERMINING THE STARTING POINT IN THE SIMULATION BY THE METHOD OF POSSIBLE DIRECTIONS

Abstract

Context. The problem of determining the starting point when of G. Zoutendijk’s method of possible directions is considered, namely the case where such a point can be arbitrary or even unknown. Presented in the article allows to determine the further direction of movement in such a way that with a minimum number of study points to obtain the most accurate result. The solution of the above problem relates to the description of complex surfaces that can be represented by a gully function. The definition of the starting point is used in the practice of modeling the development of environmental risks in technogenic pollution of intersections of territories. Objective. The solution of the problem of choosing the starting point when using the method of possible directions for describing complex surfaces ravine function. Method. The article uses the method of G. Zoutendijk for solving tasks Chebyshev’s approximation. Results. An algorithm for determining the starting point for a problem with linear constraints is introduced. An approach for solving complex tasks of representation of gully functions with the minimum possible number of iterations is presented. The results of mathematical modeling are tested in practice to solve the problem of description of the contaminated area by hydrogen’s radioisotope – tritium. Conclusions. An approach to determining the starting point in the calculations using the method of possible directions of G. Zoutendijk that allows you to select a point to build from it the motion vector with the specified step and to determine the direction of the second point to draw the next step. This takes into account the limitations, in particular – the values at each new point must be expressed in a non-negative number. For the given normalization, there are a number of features that should be taken into account in the calculation and construction of algorithms for solving applied problems according to the proposed approach. For example, some iterations can lead to more calculations and transformations on each iteration, but the number of iterations is smaller than other types of iterations. This depends on the size of the task and the number of constraints in each case. The presented approach can be used in the development of methods, models and algorithms for the description of rough terrain to solve the problems of visualization of the process of pollution by dangerous substances.