Optimal integration of highly oscillating functions in general form

Nechuiviter, Olesia; Иванов, С В; Kovalchuk, Kyrylo

doi:10.15407/fmmit2021.33.068

Fìz.-mat. model. ìnf. tehnol.

2021

DOI: 10.15407/fmmit2021.33.068

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Optimal integration of highly oscillating functions in general form

Olesia Nechuiviter

С В Иванов

Kyrylo Kovalchuk

Abstract: The development of information technology contributes to the improvement of mathematical models of phenomena and processes in many scientific areas of the technical direction. In particular, modern methods of digital signal and image processing use algorithms with new information operators. Cubature formulas are constructed for the approximate calculation of integrals of highly oscillating functions of many variables for various types of data. The paper deals with the estimation of the error in the numerical i… Show more

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2023

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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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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

Self Cite

View full text Add to dashboard Cite

show abstract

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Optimal integration of highly oscillating functions in general form

Cited by 1 publication

References 3 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

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