Recursive Algorithms for Unbalanced Banded Toeplitz Systems

Direct recursive algorithms for the solution of band Toeplitz systems are considered here. They exploit the displacement rank properties, which allow a large reduction of computational efforts and storage requirements. Their use of the Sherman-Morrison-Woodbury formula turns out 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.