A survey on recursive algorithms for unbalanced banded Toeplitz systems: computational issues

Several direct recursive algorithms for the solution of band Toeplitz systems are considered. All the methods exploit the displacement rank properties, which allow a large reduction of computational efforts and storage requirements. Some algorithms make use of the Sherman-Morrison- Woodbury formula and result to be particularly suitable for the case of unbalanced bandwidths. The computational costs of the algorithms under consideration are compared both in a theoretical and practical setting. Some stability issues are discussed as well