The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data

Regularization techniques based on the Golub-Kahan iterative bidiagonal- ization belong among popular approaches for solving large ill-posed problems. First, the original problem is projected onto a lower dimensional subspace using the bidi- agonalization algorithm, which by itself represents a form of regularization by pro- jection. The projected problem, however, inherits a part of the ill-posedness of the original problem, and therefore some form of inner regularization must be applied. Stopping criteria for the whole process are then based on the regularization of the projected (small) problem. In this paper we consider an ill-posed problem with a noisy right-hand side (ob- servation vector), where the noise level is unknown. We show how the information

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