New Information Operators in Mathematical Modeling (A Review)

Сергиенко, И. В.; Lytvyn, Oleg M.

doi:10.1007/s10559-018-0004-5

Cited by 8 publications

(3 citation statements)

References 10 publications

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“…Одним з прикладів інноваційних рішень стали нові інформаційні оператори, основні принципи побудови яких викладено в [1][2][3]. Чисельне інтегрування функцій багатьох змінних широко використовується у математичному моделюванні [4][5][6]. Окремо варто відмітити інтегрування швидко осцилюючих функцій у цифровій обробці сигналів та зображень.…”

Section: наведено оптимальну за порядком точності кубатурну формулу н...unclassified

Optimal by the Order of Accuracy Cubature Formula for the Approximate Calculation of Triple Integrals from Fast Oscillating Functions in General View

Nechuiviter,

Ivanov

2023

Cybernetics and Computer Technologies

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Introduction. The rapid development of digital technologies encourages scientists to create new or improve existing mathematical models of technical processes. It is time to develop mathematical models with different types of data. In the tasks of digital signal and image processing, the approximate calculation of integrals from rapidly oscillating functions using new information operators makes it possible to build cubature formulas using different types of information: the values of functions on planes, lines and points can be used as data. The purpose is to present and investigate the optimal cubature formula for the approximate calculation of the triple integral from rapidly oscillating functions in the general form on the class of differential functions. Information about functions are traces on systems of mutually perpendicular planes. Results. The study of the problems of digital signal and image processing continued using the example of numerical integration of triple integrals from rapidly oscillating functions in the general form. The values of functions on systems of mutually perpendicular planes are using for constructed cubature formula. The main attention in the research focuses on obtaining the estimations of errors. Proposed cubature formula for the approximate calculation of the triple integral from rapidly oscillating functions in general view is optimal in order of accuracy on the class of differential functions. The conducted numerical experiment confirmed the theoretical results. Conclusions. The obtained results make it possible to build new and improve existing mathematical models of processes with different types of input information. New information operators are a powerful tool in the development of such models. Cubature formulas for the approximate calculation of integrals from rapidly oscillating functions of many variables have been created. Іn the construction of the formulas traces of the function on planes, lines, and points are used. Formulas in their construction use function traces on planes, lines, and points. In this work, a cubature formula for the approximate calculation of the triple integral from a rapidly oscillating function in the general form, which is optimal in order of accuracy, is constructed and investigated on the class of differentiable functions. A feature of the proposed formula is the use of values of functions on systems of mutually perpendicular planes as data. Keywords: integrals of rapidly oscillating functions of many variables, cubature formulas, new information operators, digital signal and image processing.

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Section: наведено оптимальну за порядком точності кубатурну формулу н...unclassified

Optimal by the Order of Accuracy Cubature Formula for the Approximate Calculation of Triple Integrals from Fast Oscillating Functions in General View

Nechuiviter,

Ivanov

2023

Cybernetics and Computer Technologies

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“…The interconnected process of development of mathematical models, numerical algorithms, programming and creation of complexes of programs for solving these problems, their analysis, storage and output of calculation results served as a basis for new directions in scientific research. One of such directions in mathematical modeling is the theory of new information operators [1]. The new information operators give the possibility to focus on such stages of mathematical modeling as the preparation of initial information in modeling processes and phenomena, the development of algorithms for numerical problem solving, computer programming and direct calculations.…”

Section: Introductionmentioning

confidence: 99%

“…is characterized by the rapid introduction of new digital technologies, algorithms and methods. Scientists are building new or improving already known mathematical models using information technology [2]. Today many problems are being solved in cases when the input information about a function is a set of traces of the function on planes, set of traces of the function on lines or a set of values of the function in the points.…”

Section: Introductionmentioning

confidence: 99%

Application of the Theory of New Information Operators in Conducting Research in the Field of Information Technologies

Nechuiviter

2021

ITLT

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Due to the rapid development and implementation of the latest information technologies in many fields of science and technology significant changes have taken place. In particular, new mathematical theories have emerged; they can be effectively used in building and improving existing mathematical models of various phenomena and objects. Mathematical modeling is currently one of the main methods in scientific research of technological, social, economic processes and natural phenomena. No research thesis is complete without the use of mathematical methods and algorithms. In view of this it is important to acquaint young scientists with modern trends in mathematical modeling during their training for PhD degree, in particular. The development of information technology has contributed to the emergence of new approaches to obtaining, processing and analyzing information in scientific research. In this way, the theory of new information operators, which is widely used in mathematical modeling, was created. The analysis of the existing research reveals the need to consider the theoretical basics of new information operators and their application to the numerical integration of several variables functions. The example of the problem of numerical integration of two variables functions shows the way how to create cubature formulas depending on the type of the input information about function. The paper presents new cubature formulas for the approximate calculation of double integrals, in the case when the information is given by the set of traces on lines and values of the function at points. The proposed formulas have high accuracy but use much less input information compared to classical formulas for numerical integration of double integrals. All the results are supported by numerous examples made in the computer mathematics system Mathcad. The implementation of the developed methodology of using new information operators in scientific research has shown its efficacy during seminars with Master and PhD students.

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A New Approach to Data Compression

Lytvyn

2018

Advances in Intelligent Systems and Computing

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New Information Operators in Mathematical Modeling (A Review)

Cited by 8 publications

References 10 publications

Optimal by the Order of Accuracy Cubature Formula for the Approximate Calculation of Triple Integrals from Fast Oscillating Functions in General View

Optimal by the Order of Accuracy Cubature Formula for the Approximate Calculation of Triple Integrals from Fast Oscillating Functions in General View

Application of the Theory of New Information Operators in Conducting Research in the Field of Information Technologies

A New Approach to Data Compression

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