Multidimensional smoothing using hyperbolic interpolatory wavelets.
Markus Hegland, Ole M. Nielsen⋆, Zuowei Shen · ANU Open Research (Australian National University) · 2004
We propose the application of hyperbolic interpolatory wavelets for large-scale -dimensional data fitting.In particular, we show how wavelets can be used as a highly efficient tool for multidimensional smoothing.The grid underlying these wavelets is a sparse grid.The hyperbolic interpolatory wavelet space of level uses basis functions and it is shown that under sufficient smoothness an approximation error of order !can be achieved.The implementation uses the fast wavelet transform and an efficient indexing method to access the wavelet coefficients.A practical example demonstrates the efficiency of the approach.