Istituto di Informatica e Telematica     
Favati P., Lotti G., Menchi O. Solving banded Toeplitz systems. Technical report, 2005.
The solution of banded Toeplitz systems is frequently required in the applications. In this paper methods especially suited to this task are examined and compared in terms of computational costs. All the methods make use of techniques based on the displacement rank, which allow a considerable saving of the cost. A further saving of the cost is achieved by using the Sherman-Morrison-Woodbury formula for the inversions of the involved matrices. The comparisons show that a method here proposed, derived from the Stewart divide and conquer algorithm, outperforms the other methods when the bandwidths are moderately or strongly unbalanced.
Subject Banded Toeplitz matrix
Displacement structure
Sherman-Morrison-Woodbury formula
G.1.3 Numerical Linear Algebra

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