Polynomial Reproduction of Vector Subdivision Schemes
We discuss the polynomial reproduction of vector subdivision schemes with general integer dilation m≥2. We first present a simple algebraic condition for polynomial reproduction of such schemes with standard subdivision symbol. We then extend it to general subdivision symbol satisfying certain order...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/104840 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567654005604352 |
|---|---|
| author | Y. F. Shen D. H. Yuan S. Z. Yang |
| author_facet | Y. F. Shen D. H. Yuan S. Z. Yang |
| author_sort | Y. F. Shen |
| collection | DOAJ |
| description | We discuss the polynomial reproduction of vector subdivision schemes with general integer dilation m≥2. We first present a simple algebraic condition for polynomial reproduction of such schemes with standard subdivision symbol. We then extend it to general subdivision symbol satisfying certain order of sum rules. We also illustrate our results with several examples. Our results show that such kind of scheme can produce exactly the same scalar polynomial from which the data is sampled by convolving with a finite nonzero sequence of vectors. |
| format | Article |
| id | doaj-art-67eb492f188d46a5a12776371536faa0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-67eb492f188d46a5a12776371536faa02025-02-03T01:00:55ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/104840104840Polynomial Reproduction of Vector Subdivision SchemesY. F. Shen0D. H. Yuan1S. Z. Yang2Department of Mathematics, Shantou University, Shantou, Guangdong 515063, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaDepartment of Mathematics, Shantou University, Shantou, Guangdong 515063, ChinaWe discuss the polynomial reproduction of vector subdivision schemes with general integer dilation m≥2. We first present a simple algebraic condition for polynomial reproduction of such schemes with standard subdivision symbol. We then extend it to general subdivision symbol satisfying certain order of sum rules. We also illustrate our results with several examples. Our results show that such kind of scheme can produce exactly the same scalar polynomial from which the data is sampled by convolving with a finite nonzero sequence of vectors.http://dx.doi.org/10.1155/2014/104840 |
| spellingShingle | Y. F. Shen D. H. Yuan S. Z. Yang Polynomial Reproduction of Vector Subdivision Schemes Abstract and Applied Analysis |
| title | Polynomial Reproduction of Vector Subdivision Schemes |
| title_full | Polynomial Reproduction of Vector Subdivision Schemes |
| title_fullStr | Polynomial Reproduction of Vector Subdivision Schemes |
| title_full_unstemmed | Polynomial Reproduction of Vector Subdivision Schemes |
| title_short | Polynomial Reproduction of Vector Subdivision Schemes |
| title_sort | polynomial reproduction of vector subdivision schemes |
| url | http://dx.doi.org/10.1155/2014/104840 |
| work_keys_str_mv | AT yfshen polynomialreproductionofvectorsubdivisionschemes AT dhyuan polynomialreproductionofvectorsubdivisionschemes AT szyang polynomialreproductionofvectorsubdivisionschemes |