Handling Wavelet Expansions in numerical Methods

Wavelet expansions have drawn a lot of attention in recent decades. Wavelets originate from signal analysis, and one of the purposes is data compression. The ability to compress data can also be used to reduce the amount of computation work in a numerical simulation.A family of wavelets forms a basis for a function space. Most adaptive wavelet methods are based on expansions of functions in a freely selectable subset of such a basis. This avoids the often expensive, grid generation step needed in most other adaptive methods, but leads to more complicated bookkeeping.A large part of this thesis is devoted to the problem of performing this bookkeeping efficiently. Some methods divide the wavelet expansion into parts of decreasing importance. Using an approximate division is often more efficient than using the best division, which requires all terms in the expansion to be sorted.