WAVELET METHODS FOR FAST RESOLUTION OF ELLIPTIC PROBLEMS

This paper shows that the use of wavelets to discretize an elliptic problem with Dirichlet or Neumann boundary conditions has two advantages: an explicit diagonal preconditioning makes the condition number of the corresponding matrix become bounded by a constant and the order of approximation is locally of spectral type (in contrast with classical methods); using a conjugate gradient method, one thus obtains fast numerical algorithms of resolution. A comparison is also drawn between wavelet and classical methods.