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The algorithms are based on the concept of displacement structure and are valid for the more general class of Hankel\u2010like matrices. The positive\u2010definite algorithm is proven to be backward stable. The indefinite algorithm uses a look\u2010ahead step that is naturally suggested by displacement approach. Our error analysis suggests a new criterion for the size of the look\u2010ahead step and our numerical experiments suggest that the use of the new criterion allows us to ensure numerical stability in practice. 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