An implicit shift bidiagonalization algorithm for ill-posed systems
Iterative methods based on Lanczos bidiagonalization (LBD) with full reorthogonalization are considered for solving large scale discrete ill- posed linear least squares problems of the form \(\min_ x \| Ax - b \|_ 2\). Section 1 discusses the use of generalized cross-validation to estimate the optimal regularization of an LBD solution when the noise level is unknown. Section 4 studies the implicitly restarted LBD method. Section 5 explores the use of implicit restarts in the context of determining regularization parameters for the LBD, and presents some numerical examples to demonstrate their efficiency.
Lanczos bidiagonalization with full reorthogonalization
large scale discrete ill-posed linear least squares problems
scientific article; zbMATH DE number 739435
scientific article