Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials
Abstract In this paper, we construct a new family of refinable functions from generalized Bernstein polynomials, which include pseudo-splines of Type II. A comprehensive analysis of the refinable functions is carried out. We then prove the convergence of cascade algorithms associated with the new ma...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1106-0 |
| _version_ | 1819133526215229440 |
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| author | Ting Cheng Xiaoyuan Yang |
| author_facet | Ting Cheng Xiaoyuan Yang |
| author_sort | Ting Cheng |
| collection | DOAJ |
| description | Abstract In this paper, we construct a new family of refinable functions from generalized Bernstein polynomials, which include pseudo-splines of Type II. A comprehensive analysis of the refinable functions is carried out. We then prove the convergence of cascade algorithms associated with the new masks and construct Riesz wavelets whose dilation and translation form a Riesz basis for L 2 ( R ) $L_{2}(\mathbb{R})$ . Stability of the subdivision schemes, regularity and approximation orders are obtained. We also illustrate the symmetry of the corresponding refinable functions. |
| first_indexed | 2024-12-22T09:48:42Z |
| format | Article |
| id | doaj.art-6e4f41d2d00c48a4a573827753b62b06 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-22T09:48:42Z |
| publishDate | 2016-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-6e4f41d2d00c48a4a573827753b62b062022-12-21T18:30:28ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-06-012016112910.1186/s13660-016-1106-0Analysis and construction of a family of refinable functions based on generalized Bernstein polynomialsTing Cheng0Xiaoyuan Yang1Department of Mathematics, LMIB of the Ministry of Education, Beihang UniversityDepartment of Mathematics, LMIB of the Ministry of Education, Beihang UniversityAbstract In this paper, we construct a new family of refinable functions from generalized Bernstein polynomials, which include pseudo-splines of Type II. A comprehensive analysis of the refinable functions is carried out. We then prove the convergence of cascade algorithms associated with the new masks and construct Riesz wavelets whose dilation and translation form a Riesz basis for L 2 ( R ) $L_{2}(\mathbb{R})$ . Stability of the subdivision schemes, regularity and approximation orders are obtained. We also illustrate the symmetry of the corresponding refinable functions.http://link.springer.com/article/10.1186/s13660-016-1106-0refinable functionsgeneralized Bernstein polynomialscascade algorithmsRiesz wavelet bases |
| spellingShingle | Ting Cheng Xiaoyuan Yang Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials Journal of Inequalities and Applications refinable functions generalized Bernstein polynomials cascade algorithms Riesz wavelet bases |
| title | Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials |
| title_full | Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials |
| title_fullStr | Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials |
| title_full_unstemmed | Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials |
| title_short | Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials |
| title_sort | analysis and construction of a family of refinable functions based on generalized bernstein polynomials |
| topic | refinable functions generalized Bernstein polynomials cascade algorithms Riesz wavelet bases |
| url | http://link.springer.com/article/10.1186/s13660-016-1106-0 |
| work_keys_str_mv | AT tingcheng analysisandconstructionofafamilyofrefinablefunctionsbasedongeneralizedbernsteinpolynomials AT xiaoyuanyang analysisandconstructionofafamilyofrefinablefunctionsbasedongeneralizedbernsteinpolynomials |