Особливості алгоритмізації процесів мінімізації похибок апроксимації при вирішенні прикладних задач

Abstract

The paper defines the mathematical features arising during the algorithmization of the minimi-zation of errors that appear as a result of the approximation of functions in applied environmen-tal safety problems, the creation of automated personnel selection systems, and the improve-ment of systems with a recommendation mechanism. It has been proved that when performing the algorithmization of any process, it is necessary to take into account the ignoring of some part of the information in the process of formalization. When transforming information, any event in the process of functioning of a complex system over a certain period of time can be considered as the occurrence of a specific situation at some specified point, to which the re-quirements for ensuring the properties of information are put forward. The work is based on the basic postulates of the Cauchy theorem and Dr. Tesler's works on some assertions on the de-composition of functions by incoherence. Using the approach to solving problems with complex variants of approximation of functions and existing methods of minimizing errors in approxi-mations, there is proposed an algorithm that in the case of finding a solution with a large num-ber of iterations allows for carrying out a number of transformations that will let obtain the re-sult through expansion in the Taylor series by degrees. It has been found that in the absence of a clear solution to the given problem, it is best to use an approximation with some incoherence. That means choosing a parameter that acts as an element of adaptation to the specified condi-tions of the task. Of course, this method of problem solving requires functional transformations, but in the end, it allows you to use basic trigonometric functions that simplify algorithmization. An example of a practical implementation of the algorithm with the minimization of approxi-mation errors has been considered. Based on it, it has been proved that it is more rational to use tables of a number of widely used functions and decompose functions into series by errors.