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The Cascade Algorithm for the Numerical Computation of Refinable Functions

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Abstract

The cascade algorithm is a method which can be used for the computation of refinable functions. We prove here that in general the cascade algorithm will not inherit the accuracy and refinability of the limit refinable function. We provide conditions for which the cascade iteration does indeed preserve accuracy.

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References

  1. A.S. Cavaretta, W. Dahmen and C.A. Micchelli, Stationary subdivision, Mem. Amer. Math. Soc. 93(453) (1991) 1–186.

    Google Scholar 

  2. D.R. Chen, R.Q. Jia and S.D. Riemenschneider, Convergence of vector subdivision schemes in Sobolev spaces, Appl. Comput. Harmon. Anal. 12 (2002) 128–149.

    Google Scholar 

  3. R.Q. Jia, Approximation properties of multivariate wavelets, Math. Comp. 67 (1998) 647–665.

    Google Scholar 

  4. C.A. Micchelli, Mathematical Aspects of Geometric Modeling, CBMS, Vol. 65 (SIAM, Philadelphia, PA, 1995).

    Google Scholar 

  5. C.A. Micchelli and H. Prautzsch, Uniform refinement of curves, Linear Algebra Appl. 114/115 (1989) 161–194.

    Google Scholar 

  6. C.A. Micchelli and T. Sauer, Regularity of multiwavelets, Adv. Comput. Math. 7 (1997) 455–546.

    Google Scholar 

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Authors and Affiliations

  1. Department of Scientific Computing and Computer Applications, Zhongshan University, Guangzhou, 510275, P. R. China

    Qiuhui Chen

  2. Department of Mathematics, West Virginia University, Morgantown, WV, 26506, USA

    Yuesheng Xu

  3. Institute of Mathematics, Academy of Mathematics and System Science, Chinese Academy of Science, Beijing, 100080, P. R. China

    Yuesheng Xu

Authors
  1. Qiuhui Chen
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  2. Yuesheng Xu
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Chen, Q., Xu, Y. The Cascade Algorithm for the Numerical Computation of Refinable Functions. Advances in Computational Mathematics 20, 17–24 (2004). https://doi.org/10.1023/A:1025844410775

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  • DOI: https://doi.org/10.1023/A:1025844410775

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