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Shen, Y. F.; Yuan, D. H.; Yang, S. Z.

Polynomial reproduction of vector subdivision schemes. (English) Zbl 1470.41010

Abstr. Appl. Anal. 2014, Article ID 104840, 10 p. (2014).
Summary: We discuss the polynomial reproduction of vector subdivision schemes with general integer dilation \(m \geq 2\). 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.

MSC:

41A30 Approximation by other special function classes
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets
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