Computation with wavelets in higher dimensions.

In dimension d, a lattice grid of size N has N points. The representation of a function by, for instance, splines or the so-called non-standard wavelets with error ǫ would require O(ǫ) lattice point values (resp. wavelet coefficients), for some positive a depending on the spline order (resp. the properties of the wavelet). Unless d 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 N or ǫ. I will discuss how to organize the wavelets so that functions can be represented with O((log(1/ǫ))ǫ) coefficients. Using wavelet packets, the number of coefficients may be further reduced. 1991 Mathematics Subject Classification: Primary Secondary