Using Core Formulations for Ill-posed Linear Systems

We investigate the application of core problem formulations to the context of ill-posed linear algebraic systems. We note that in order to impose regularization on such systems by using core formulations, one is lead to a technique similar to the Truncated (Total) Least Squares method. Choosing an appropriate truncation level from given data can be made efficient by incorporating the truncation level decision as a stopping criterion into a partial bidiagonalization algorithm. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)