LBAS: Lanczos Bidiagonalization with Subspace Augmentation for Discrete Inverse Problems

The regularizing properties of Lanczos bidiagonalization are powerful when the underlying Krylov subspace captures the dominating components of the solution. In some applications the regularized solution can be further improved by augmenting the Krylov subspace with a low-dimensional subspace that represents specific prior information. Inspired by earlier work on GMRES we demonstrate how to carry these ideas over to the Lanczos bidiagonalization algorithm