Automatic stopping rule for iterative methods in discrete ill-posed problems
This paper deals with the underlying properties of a stopping rule for the least squares QR-methods proposed recently by \textit{F. S. V. Bazán} et al. [Numer. Linear Algebra Appl. 21, No. 3, 316--339 (2014; Zbl 1340.65071)], and shows how to extend it to Krylov subspace projection methods such as the generalized minimal residual method, the minimal residual method, etc., for which regularization is achieved by projecting the original problem onto a Krylov subspace and where the dimension of this subspace plays the role of the regularization parameter. The authors also consider how to apply the rule to certain preconditioned versions of these methods. Like the original rule, the extended version works well without requiring a priori knowledge about the error norm.
scientific article; zbMATH DE number 6497596
scientific article