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Abstract and Applied Analysis
Volume 2014, Article ID 104840, 10 pages
http://dx.doi.org/10.1155/2014/104840
Research Article

Polynomial Reproduction of Vector Subdivision Schemes

1Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China
2Department of Mathematics, Dezhou University, Dezhou 253023, China
3Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, China

Received 1 April 2014; Accepted 25 May 2014; Published 7 July 2014

Academic Editor: Wenchang Sun

Copyright © 2014 Y. F. Shen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss the polynomial reproduction of vector subdivision schemes with general integer dilation . 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.