A multilevel augmentation method for solving ill-posed operator equations

Abstract

We introduce a multilevel augmentation method for solving ill-posed operator equations by making use of the multiscale structure of the matrix representation of the operator. The method leads to fast solutions of the discrete regularization methods for the equations. Choices for a priori and a posteriori regularization parameters are proposed. An optimal convergence order for the method with the choices of parameters is established. Numerical results are presented to illustrate the accuracy and efficiency of the method.