Abstract
Two algorithms of the Levinson type for the solution of general Toeplitz systems are considered. The second one is better suited for vector computers while the first one is faster on scalar machines. They can break down, or behave poorly, when some of the leading principal submatrices are singular, or ill conditioned, although the whole matrix is very well conditioned. A perturbation approach is shown to work well in this case for both algorithms. The number of the additional flops can be relatively small in comparison to the look-ahead strategies.
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