Open AccessAn algorithm for constructing a direct and inverse operator of a real process
Author(s) -
L. T. Boyko,
A. A. Kochuk
Publication year - 2019
Publication title -
pitannâ prikladnoï matematiki ì matematičnogo modelûvannâ
Language(s) - English
Resource type - Journals
ISSN - 2074-5893
DOI - 10.15421/321903
Subject(s) - operator (biology) , algorithm , tikhonov regularization , computer science , algebraic equation , process (computing) , regularization (linguistics) , task (project management) , mathematics , mathematical optimization , inverse problem , artificial intelligence , nonlinear system , mathematical analysis , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene , operating system , management , economics
Consider the task of building a mathematical model of the real process, which translates the data at the entrance to a certain result at the output. Considered the case when severaldata is submitted to the entrance, and the output result is only one. The direct operator of the real process makes it possible to determine (provide) the result at the exit based on the known data at the entrance. The reverse operator on a known result on the way out of the real process allows you to find the necessary input. Operators of the real process are modeled with algebraic polynom to some extent. The degree of algebraic polynomic and its coefficients depend on a specific real process. Since input and output are known with some error in real-world processes, we take into account input and output errors when building operators. The task of building such operators is incorrect on Adamar, so we use the method of regularization of Tikhonov. This method allows you to build sustainable approach (taking into account the error of the input and output data) the right operators. The article examines in detail the algorithm for building a reverse operator. The direct operator algorithm is reviewed in the authors' previous article (link [2] in this article). Building a reverse operator comes down to solving a non-linear equation in an incorrect setting. The non-linear equation is solved by Newton's iterative method. The software implementation of the algorithm has been carried out. Three test examples are considered, which confirm the correctness of the algorithm and program. The algorithm can be summarized in case there are several data (at least two) at both the entrance and exit.