A new wavelet preconditioner for finite difference operators
The paper deals with a multiscale preconditioner for finite difference approximations of variable coefficient problems in one space dimension. The authors use the properties of compactly supported regular wavelets that allow to cure the ill-conditioning due to differentiation as well as the ill-conditioning due to multiplication by a variable coefficient. The implementation of this construction can be made fast thanks to a hierarchical decomposition of the operators involving filters related to the fast wavelet transform. Numerical tests show the efficiency of the presented construction as well as its flexibility which is a property not shared by other multiscale preconditioners
scientific article; zbMATH DE number 2140537