Analysis of the Results of a Computing Experiment to Restore the Discontinuous Functions of Two Variables Using Projections. III

This article continues a series of publications under the same name. It performs further improvement of the method for restoring discontinuous functions of two variables using projections to improve the accuracy of approximation without the Gibbs phenomenon for the case, where the discontinuity line...

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Bibliographic Details
Published inCybernetics and systems analysis Vol. 58; no. 3; pp. 372 - 381
Main Authors Lytvyn, O. M., Lytvyn, O. G.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2022
Springer
Springer Nature B.V
Subjects
Approximation
Artificial Intelligence
Computation
Control
Discontinuity
Gibbs phenomenon
Mathematics
Mathematics and Statistics
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
computed tomography
differentiability class
Gibbs phenomenon
discontinuous spline
discontinuous function
Fourier sum
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Summary:This article continues a series of publications under the same name. It performs further improvement of the method for restoring discontinuous functions of two variables using projections to improve the accuracy of approximation without the Gibbs phenomenon for the case, where the discontinuity lines are the boundaries of squares nested into each other. We consider the case of the discontinuity lines having angular points, where the derivative along the normal is undefined. A discontinuous spline is constructed so that the difference between the function being approximated and this spline is a differentiable function. This function is restored using finite Fourier sums whose Fourier coefficients are found using projections. Analysis of the computing results confirmed the theoretical statement of the study.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-022-00469-8