Decay characteristics of the hat interpolation wavelet coefficients in the two-dimensional multiresolution representation

Kiwoon Kwon, Yoon Young Kim

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)305-334
Number of pages30
JournalJournal of the Korean Mathematical Society
Volume42
Issue number2
DOIs
StatePublished - Mar 2005

Keywords

  • Adaptive wavelet-Galerkin method
  • Decay characteristics
  • Hat interpolation wavelet

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