Science China Mathematics

, Volume 55, Issue 3, pp 577–592 | Cite as

Convergence and error estimate of cascade algorithms with infinitely supported masks in L p (ℝ s )

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Abstract

The cascade algorithm plays an important role in computer graphics and wavelet analysis. In this paper, we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a general dilation matrix in L p (ℝ s ) (1 ⩾ p ⩾ ∞) spaces, and then we give an error estimate of the cascade algorithms associated with truncated masks. It is proved that under some appropriate conditions if the cascade algorithm associated with a polynomially decaying mask converges in the L p -norm, then the cascade algorithms associated with the truncated masks also converge in the L p -norm. Moreover, the error between the two resulting limit functions is estimated in terms of the masks.

Keywords

cascade algorithm polynomially decaying masks error estimate 

MSC(2010)

26A16 26A18 39B12 41A25 42B15 65D05 
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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesHohai UniversityNanjingChina
  2. 2.Department of Mathematics, College of SciencesZhejiang UniversityHangzhouChina

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