Tikhonov regularization via flexible Arnoldi reduction

Flexible GMRES, introduced by Saad, is a generalization of the standard GMRES method for the solution of large linear systems of equations. It is based on the flexible Arnoldi process for reducing a large square matrix to a small matrix. We describe how the flexible Arnoldi process can be applied to implement one-parameter and multi-parameter Tikhonov regularization of linear discrete ill-posed problems. The method proposed is well suited for large-scale problems. Moreover, computed examples show that our method can give approximate solutions of higher accuracy than available direct methods for small-scale problems.