Cubic spline wavelet bases of sobolev spaces and multilevel interpolation

Abstract

In this paper, a semi-orthogonal cubic spline wavelet basis of homogeneous Sobolev space H20(I) is constructed, which turns out to be a basis of the continuous space C0(I). At the same time, the orthogonal projections on the wavelet subspaces in H20(I) are extended to the interpolating operators on the corresponding wavelet subspaces in C0(I). A fast discrete wavelet transform (FWT) for functions in C0(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. © 1996 Academic Press, Inc.