An implicit wavelet sparse approximate inverse preconditioner

Wavelet-based sparse approximate inverse preconditioners are considered for the linear system Ax = b. The preconditioners are good sparse approximations to the inverse of A computed by taking advantage of the compression obtained by working in a wavelet basis. When the representation of A in a single scale basis (for example, a finite element basis) is available, the formulation presented obviates computation of the representation of A in the wavelet basis and removes the associated costs. Efficient application for both sparse and dense A is considered.