Examining a mathematical apparatus of Z-approximation of functions for the construction of an adaptive algorithm

Kryazhych, Olha; Kovalenko, O. V.

doi:10.15587/1729-4061.2019.170824

Cited by 2 publications

(2 citation statements)

References 4 publications

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“…However, this is not the end of the task. Now it is necessary to obtain unconditional optimal equations by way from beginning to end along a chain: This approach makes it possible to consider applied technical problems, for example, the problem of designing a service-oriented network [18], developing a recommendation system for a bank or credit institution [19], personnel selection systems for many heterogeneous parameters [20], or developing a model for the spread of environmental pollution [21,22].…”

Section: Bellman Functional Equationmentioning

confidence: 99%

Features in solving individual tasks to develop service-oriented networks using dynamic programming

Kryazhych

Itskovych

Iushchenko

et al. 2023

EEJET

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The object of this study is an approach to solving the problems of designing service-oriented networks that warn about emergencies using dynamic programming. The main issue is the complexity of algorithmization of processes that describe the achievement of an optimal solution in multi-stage nonlinear problems. The possibilities of applying the Bellman optimality principle for solving the set tasks for the purpose of their application in the field of engineering and technology are determined. Based on the Bellman functional equation, a model of the optimal number of sensors in the monitoring system for warning of emergencies was built. A feature of the design is that using the classical Bellman equation, it is proposed to solve problems of various technical directions, provided that the resource determines what exactly makes it possible to optimize work in any way. Important with this approach is the planning of the action as an element of some problem with the augmented state. After that, the proposed structure in formal form extends to other objects. A problem was proposed and considered, which confirmed the mathematical calculations, as a result of which an optimal plan for replacing the sensors of the system was obtained; and the possibilities of significant cost reduction were identified. In the considered example, an optimal plan for replacing the system sensors was compiled and the possibility of reducing costs by 31.9 % was proved. The proposed option was used in the development of information technology for modeling a service-oriented network based on energy-efficient long-range protocols; some of the identified features were further developed in the design of a recommendation system for issuing loans and developing an interactive personnel training system

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Section: Bellman Functional Equationmentioning

confidence: 99%

Features in solving individual tasks to develop service-oriented networks using dynamic programming

Kryazhych

Itskovych

Iushchenko

et al. 2023

EEJET

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“…Існують багато прикладів [8][9][10] алгоритмізації апроксимації функцій для вирішення прикладних задач, де зазначається, що питання мінімізації похибок є актуальним і потребує пошуку рішення при алгоритмізації процесів. Серед дослідників, що займалися вирішенням цієї задачі, можна назвати Шора Н.З.…”

Section: вступunclassified

Features of the algorithmization of the processes of minimization of approximation errors when solving applied problems

Kryazhych¹,

Iushchenko²,

Itskovych³

et al. 2023

MMS

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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.

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Examining a mathematical apparatus of Z-approximation of functions for the construction of an adaptive algorithm

Cited by 2 publications

References 4 publications

Features in solving individual tasks to develop service-oriented networks using dynamic programming

Features in solving individual tasks to develop service-oriented networks using dynamic programming

Features of the algorithmization of the processes of minimization of approximation errors when solving applied problems

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