Improving the numerical stability of fast algorithms by square-root factorization generally requires the use of hypernormal transformations which do not always exhibit a satisfactory numerical behavior. An alternate approach, adapted from a paper by A.W. Bojanczyk and A. O. Steinhardt (see ibid., vol.37, p.1286-8, 1989), is proposed. It uses orthogonal transformations, which leads to more stable fast square-root algorithms. Applications to the generalized Levinson algorithm and the Chandrasekhar equations are detailed.
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