A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization

Summary. An additive Schwarz iteration is described for the fast resolution of linear ill-posed problems which are stabilized by Tikhonov regularization. The algorithm and its analysis are presented in a general framework which applies to integral equations of the first kind discretized either by spline functions or Daubechies wavelets. Numerical experiments are reported on to illustrate the theoretical results and to compare both discretization schemes. Received March 6, 1995 / Revised version received December 27, 1995