Direct Algorithm for Bernstein Enclosure Boundary of Polynomials
Multivariate polynomials of finite degree can be expanded into Bernstein form over a given simplex domain. The minimum and maximum Bernstein control points optimize the polynomial curve over the same domain. In this paper, we address methods for computing these control points in the simplicial case...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9156188 |
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| _version_ | 1850227192647122944 |
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| author | Tareq Hamadneh Hassan Al Zoubi Ibraheem Abu Falahah Mutaz Al-Sabbagh |
| author_facet | Tareq Hamadneh Hassan Al Zoubi Ibraheem Abu Falahah Mutaz Al-Sabbagh |
| author_sort | Tareq Hamadneh |
| collection | DOAJ |
| description | Multivariate polynomials of finite degree can be expanded into Bernstein form over a given simplex domain. The minimum and maximum Bernstein control points optimize the polynomial curve over the same domain. In this paper, we address methods for computing these control points in the simplicial case of maximum degree L. To this end, we provide arithmetic operations and properties for obtaining a fast computational method of Bernstein coefficients. Furthermore, we give an algorithm for direct determination of the minimum and maximum Bernstein coefficients (enclosure boundary) in the simplicial multivariate case. Subsequently, the implicit form, monotonicity, and dominance cases are investigated. |
| format | Article |
| id | doaj-art-1746ed02e8db4154916b9d363207df9e |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-1746ed02e8db4154916b9d363207df9e2025-08-20T02:04:54ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9156188Direct Algorithm for Bernstein Enclosure Boundary of PolynomialsTareq Hamadneh0Hassan Al Zoubi1Ibraheem Abu Falahah2Mutaz Al-Sabbagh3Al Zaytoonah University of JordanAl Zaytoonah University of JordanThe Hashemite UniversityDepartment of Basic EngineeringMultivariate polynomials of finite degree can be expanded into Bernstein form over a given simplex domain. The minimum and maximum Bernstein control points optimize the polynomial curve over the same domain. In this paper, we address methods for computing these control points in the simplicial case of maximum degree L. To this end, we provide arithmetic operations and properties for obtaining a fast computational method of Bernstein coefficients. Furthermore, we give an algorithm for direct determination of the minimum and maximum Bernstein coefficients (enclosure boundary) in the simplicial multivariate case. Subsequently, the implicit form, monotonicity, and dominance cases are investigated.http://dx.doi.org/10.1155/2022/9156188 |
| spellingShingle | Tareq Hamadneh Hassan Al Zoubi Ibraheem Abu Falahah Mutaz Al-Sabbagh Direct Algorithm for Bernstein Enclosure Boundary of Polynomials Journal of Mathematics |
| title | Direct Algorithm for Bernstein Enclosure Boundary of Polynomials |
| title_full | Direct Algorithm for Bernstein Enclosure Boundary of Polynomials |
| title_fullStr | Direct Algorithm for Bernstein Enclosure Boundary of Polynomials |
| title_full_unstemmed | Direct Algorithm for Bernstein Enclosure Boundary of Polynomials |
| title_short | Direct Algorithm for Bernstein Enclosure Boundary of Polynomials |
| title_sort | direct algorithm for bernstein enclosure boundary of polynomials |
| url | http://dx.doi.org/10.1155/2022/9156188 |
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