Computation with wavelets in higher dimensions
In dimension , a lattice grid of size has points. The representation of a function by, for instance, splines or the so-called non-standard wavelets with error would require lattice point values (resp. wavelet coefficients), for some positive depending on the spline order (resp. the properties of the wavelet). Unless is very small, we easily will get a data set that is larger than a computer in practice can handle, even for very moderate choices of or . I discuss how to organize the wavelets so that functions can be represented with coefficients. Using wavelet packets, the number of coefficients may be further reduced.