Solution to the problem of instability in banded Toeplitz solvers

The author presents a numerically stable approach to solving banded Toeplitz systems of n linear equations. The algorithm is fast in that it requires only O(nq) operations, where q is the bandwidth of the matrix. An earlier version of the banded Toeplitz algorithm presented in the literature suffers from numerical instability. The author solves the instability problem by developing numerically stable alternatives to the back substitution process. These new algorithms have roughly the same number of calculations as simple back substitution, O(nq), and therefore can be used effectively in place of back substitution. The stabilization procedures described have been used to find accurate solutions to systems of order several thousand