TY - JOUR
T1 - Decay characteristics of the hat interpolation wavelet coefficients in the two-dimensional multiresolution representation
AU - Kwon, Kiwoon
AU - Kim, Yoon Young
PY - 2005/3
Y1 - 2005/3
N2 - 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.
AB - 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.
KW - Adaptive wavelet-Galerkin method
KW - Decay characteristics
KW - Hat interpolation wavelet
UR - http://www.scopus.com/inward/record.url?scp=20744434387&partnerID=8YFLogxK
U2 - 10.4134/JKMS.2005.42.2.305
DO - 10.4134/JKMS.2005.42.2.305
M3 - Article
AN - SCOPUS:20744434387
SN - 0304-9914
VL - 42
SP - 305
EP - 334
JO - Journal of the Korean Mathematical Society
JF - Journal of the Korean Mathematical Society
IS - 2
ER -