Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DECAY CHARACTERISTICS OF THE HAT INTERPOLATION WAVELET COEFFICIENTS IN THE TWO-DIMENSIONAL MULTIRESOLUTION REPRESENTATION

  • KWON KIWOON (Institute fur Numerische und Angewandte Mathematik Georg-August-Universitat Gottingen) ;
  • KIM YOON YOUNG (School of Mechanical and Aerospace Engineering Seoul NationalUniversity)
  • Published : 2005.02.01
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Abstract

The objective of this study is to analyze the decay characteristics of the hat interpolation wavelet coefficients of some smooth functions defined in a two-dimensional space. The motivation of this research is to establish some fundamental mathematical foundations needed in justifying the adaptive multiresolution analysis of the hat-interpolation wavelet-Galerkin method. Though the hat-interpolation wavelet-Galerkin method has been successful in some classes of problems, no complete error analysis has been given yet. As an effort towards this direction, we give estimates on the decaying ratios of the wavelet coefficients at children interpolation points to the wavelet coefficient at the parent interpolation point. We also give an estimate for the difference between non-adaptively and adaptively interpolated representations.

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References

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