Polynomial Reproduction of Vector Subdivision Schemes. (7th July 2014)

• Record Type: Journal Article
• Authors: Shen, Y. F.; Yuan, D. H.; Yang, S. Z.
• Other Names: Sun Wenchang Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-07-07
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/104840
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We discuss the polynomial reproduction of vector subdivision schemes with general integer dilationm ≥ 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.