Application of Bernstein polynomials to suppress the Gibbs effect (literature review)
Background. Despite Gibbs effect (phenomenon) was discovered almost 170 years ago, the amount of works devoted to its research and the construction of methods of its suppression has not weakened until recently. This is due to the fact that the Gibbs effect has a negative impact on the study of ma...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Penza State University Publishing House
2022-01-01
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| Series: | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
| Subjects: |
| _version_ | 1818249246243028992 |
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| author | I.V. Boykov G.Yu. Salimov |
| author_facet | I.V. Boykov G.Yu. Salimov |
| author_sort | I.V. Boykov |
| collection | DOAJ |
| description | Background. Despite Gibbs effect (phenomenon) was discovered almost 170
years ago, the amount of works devoted to its research and the construction of methods of
its suppression has not weakened until recently. This is due to the fact that the Gibbs effect
has a negative impact on the study of many wave processes in hydrodynamics,
electrodynamics, microwave technology, and computational mathematics. Therefore, the
construction of new methods for suppressing the Gibbs effect is an issue of the day.
In addition, several computational schemes for solving the Gibbs problem in one particular formulation are proposed. Materials and methods. Methods of approximation theory were
used in the construction of computational schemes. In particular, the properties of Bernstein
polynomials were used in the approximation of integer functions. Results. The review of
works devoted to the study of the Gibbs effect and methods of constructing filters that
suppress this effect is presented. The review includes: historical background on the study of
the Gibbs effect; various methods of suppressing the Gibbs effect; methods of building
filters; descriptions of the manifestation of the Gibbs effect in technology. Conclusions.
The possibility of applying Bernstein polynomials to the solution of the Gibbs problem in
the case of analytic nonperiodic functions given by values in equally spaced nodes is
demonstrated. These results can be used in solving the problem of suppressing the Gibbs
effect in other formulations. |
| first_indexed | 2024-12-12T15:33:26Z |
| format | Article |
| id | doaj.art-995c645c572d42c1b6742d8e0e3ca7ed |
| institution | Directory Open Access Journal |
| issn | 2072-3040 |
| language | English |
| last_indexed | 2024-12-12T15:33:26Z |
| publishDate | 2022-01-01 |
| publisher | Penza State University Publishing House |
| record_format | Article |
| series | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
| spelling | doaj.art-995c645c572d42c1b6742d8e0e3ca7ed2022-12-22T00:20:04ZengPenza State University Publishing HouseИзвестия высших учебных заведений. Поволжский регион: Физико-математические науки2072-30402022-01-01410.21685/2072-3040-2021-4-7Application of Bernstein polynomials to suppress the Gibbs effect (literature review)I.V. Boykov0G.Yu. Salimov1Penza State UniversityPenza State UniversityBackground. Despite Gibbs effect (phenomenon) was discovered almost 170 years ago, the amount of works devoted to its research and the construction of methods of its suppression has not weakened until recently. This is due to the fact that the Gibbs effect has a negative impact on the study of many wave processes in hydrodynamics, electrodynamics, microwave technology, and computational mathematics. Therefore, the construction of new methods for suppressing the Gibbs effect is an issue of the day. In addition, several computational schemes for solving the Gibbs problem in one particular formulation are proposed. Materials and methods. Methods of approximation theory were used in the construction of computational schemes. In particular, the properties of Bernstein polynomials were used in the approximation of integer functions. Results. The review of works devoted to the study of the Gibbs effect and methods of constructing filters that suppress this effect is presented. The review includes: historical background on the study of the Gibbs effect; various methods of suppressing the Gibbs effect; methods of building filters; descriptions of the manifestation of the Gibbs effect in technology. Conclusions. The possibility of applying Bernstein polynomials to the solution of the Gibbs problem in the case of analytic nonperiodic functions given by values in equally spaced nodes is demonstrated. These results can be used in solving the problem of suppressing the Gibbs effect in other formulations.gibbs effectfiltersbernstein polynomial |
| spellingShingle | I.V. Boykov G.Yu. Salimov Application of Bernstein polynomials to suppress the Gibbs effect (literature review) Известия высших учебных заведений. Поволжский регион: Физико-математические науки gibbs effect filters bernstein polynomial |
| title | Application of Bernstein polynomials to suppress the Gibbs effect (literature review) |
| title_full | Application of Bernstein polynomials to suppress the Gibbs effect (literature review) |
| title_fullStr | Application of Bernstein polynomials to suppress the Gibbs effect (literature review) |
| title_full_unstemmed | Application of Bernstein polynomials to suppress the Gibbs effect (literature review) |
| title_short | Application of Bernstein polynomials to suppress the Gibbs effect (literature review) |
| title_sort | application of bernstein polynomials to suppress the gibbs effect literature review |
| topic | gibbs effect filters bernstein polynomial |
| work_keys_str_mv | AT ivboykov applicationofbernsteinpolynomialstosuppressthegibbseffectliteraturereview AT gyusalimov applicationofbernsteinpolynomialstosuppressthegibbseffectliteraturereview |