Rounding Errors in Solving Block Hessenberg Systems

A rounding error analysis is presented for a divide-and-conquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a backward stable solution. The algorithm is shown to be stable for diagonally dominant matrices and for M-matrices. (Also cross-referenced as UMIACS-TR-94-105

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