Projected Tikhonov Regularization of Large-Scale Discrete Ill-Posed Problems

The solution of linear discrete ill-posed problems is very sensitive to perturbations in the data. Confidence intervals for solution coordinates provide insight into the sensitivity. This paper presents an efficient method for computing confidence intervals for large-scale linear discrete ill-posed problems. The method is based on approximating the matrix in these problems by a partial singular value decomposition of low rank. We investigate how to choose the rank. Our analysis also yields novel approaches to the solution of linear discrete ill-posed problems with solution norm or residual norm constraints.