Interpolating cubic spline wavelet packet on arbitrary partitions

In many applications, the splines on an arbitrary partition are very useful. In this paper, a spline wavelet structure is created in the way that it provides a multi-resolution approximation of the spline subspaces with arbitrary partition in the space of continuous functions on a finite interval. Based on the wavelet basis and the wavelet packet in this structure, a multi-level interpolation method is developed for decomposing a function into wavelet series and reconstructing it from its wavelet representation.