Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. Traditionally hybrid LSQR iterative methods are used to find the solution on a subspace that inherits the ill-conditioning of the original problem and regularization is imposed at the subspace level. Modern techniques employ a randomized singular value decomposition (RSVD) to find the subspace for the solution. Through the connection with the truncated singular value decomposition we prove parameter convergence for the hybrid RSVD approaches.

This presentation is part of Minisymposium “MS8 - Krylov Methods in Imaging: Inverse Problems, Data Assimilation, and Uncertainty Quantification (2 parts)”
organized by: Arvind Saibaba (North Carolina State University) , Julianne Chung (Virginia Tech) , Eric de Sturler (Virginia Tech) .

Authors:

Rosemary Renaut (Arizona State University)

Anthony Helmstetter (Arizona State University)

Saeed Vatankhah (University of Tehran)

Keywords:

inverse problems, numerical linear algebra