Integral method from even to odd order for trigonometric B-spline basis
The conventional trigonometric B-spline basis of odd order for piecewise trigonometric polynomial space possesses a lot of good modeling properties. However, its order cannot be increased by the integral method like B-spline because of the particularity of the trigonometric polynomials. In the paper...
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AIMS Press
2024-12-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241729 |
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| author | Mei Li Wanqiang Shen |
| author_facet | Mei Li Wanqiang Shen |
| author_sort | Mei Li |
| collection | DOAJ |
| description | The conventional trigonometric B-spline basis of odd order for piecewise trigonometric polynomial space possesses a lot of good modeling properties. However, its order cannot be increased by the integral method like B-spline because of the particularity of the trigonometric polynomials. In the paper, a basis in an even-order trigonometric polynomial space is defined, and its integral relation with the existing odd-order trigonometric B-spline basis is obtained. First, the condition of the knot sequence is improved to ensure the nonnegativity of the prior odd-order trigonometric B-spline basis. Under the revised condition, a set of truncation functions is given and used to build a basis for piecewise trigonometric polynomial space without constant terms, which is also known as the direct current (DC) component-free space, secondly. The basis fulfills local support and continuity properties like B-spline of even order, and each basis function is unique under a constant multiple. Thirdly, the integral formula from the even-order to odd-order trigonometric B-spline basis is proved. |
| format | Article |
| id | doaj-art-8745a1601bbe41b8afac43d043bb0329 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj-art-8745a1601bbe41b8afac43d043bb03292025-01-23T07:53:26ZengAIMS PressAIMS Mathematics2473-69882024-12-01912364703649210.3934/math.20241729Integral method from even to odd order for trigonometric B-spline basisMei Li0Wanqiang Shen1School of Science, Jiangnan University, Wuxi 214122, ChinaSchool of Science, Jiangnan University, Wuxi 214122, ChinaThe conventional trigonometric B-spline basis of odd order for piecewise trigonometric polynomial space possesses a lot of good modeling properties. However, its order cannot be increased by the integral method like B-spline because of the particularity of the trigonometric polynomials. In the paper, a basis in an even-order trigonometric polynomial space is defined, and its integral relation with the existing odd-order trigonometric B-spline basis is obtained. First, the condition of the knot sequence is improved to ensure the nonnegativity of the prior odd-order trigonometric B-spline basis. Under the revised condition, a set of truncation functions is given and used to build a basis for piecewise trigonometric polynomial space without constant terms, which is also known as the direct current (DC) component-free space, secondly. The basis fulfills local support and continuity properties like B-spline of even order, and each basis function is unique under a constant multiple. Thirdly, the integral formula from the even-order to odd-order trigonometric B-spline basis is proved.https://www.aimspress.com/article/doi/10.3934/math.20241729trigonometric b-splinenonnegativityknot sequencetruncation functionintegral formula |
| spellingShingle | Mei Li Wanqiang Shen Integral method from even to odd order for trigonometric B-spline basis AIMS Mathematics trigonometric b-spline nonnegativity knot sequence truncation function integral formula |
| title | Integral method from even to odd order for trigonometric B-spline basis |
| title_full | Integral method from even to odd order for trigonometric B-spline basis |
| title_fullStr | Integral method from even to odd order for trigonometric B-spline basis |
| title_full_unstemmed | Integral method from even to odd order for trigonometric B-spline basis |
| title_short | Integral method from even to odd order for trigonometric B-spline basis |
| title_sort | integral method from even to odd order for trigonometric b spline basis |
| topic | trigonometric b-spline nonnegativity knot sequence truncation function integral formula |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241729 |
| work_keys_str_mv | AT meili integralmethodfromeventooddorderfortrigonometricbsplinebasis AT wanqiangshen integralmethodfromeventooddorderfortrigonometricbsplinebasis |