Cubic Spline Wavelet Bases of Sobolev Spaces and Multilevel Interpolation
✍ Scribed by Jianzhong Wang
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 235 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1063-5203
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✦ Synopsis
In this paper, a semi-orthogonal cubic spline wavelet basis of homogeneous Sobolev space H 2 0 (I) is constructed, which turns out to be a basis of the continuous space C 0 (I). At the same time, the orthogonal projections on the wavelet subspaces in H 2 0 (I) are extended to the interpolating operators on the corresponding wavelet subspaces in C 0 (I). A fast discrete wavelet transform (FWT) for functions in C 0 (I) is also given, which is different from the pyramid algorithm and easy to perform using a parallel algorithm. Finally, it is shown that the singularities of a function can be traced from its wavelet coefficients, which provide an adaptive approximation scheme allowing us to reduce the operation time in computation.