IMPROVED SQUARE-ROOT FORMS OF FAST LINEAR LEAST-SQUARES ESTIMATION ALGORITHMS

Square-root factorization is one of the general ways of improving the numerical stability of fast algorithms, though it generally requires the use of hypernormal transformations which do not always exhibit a satisfactory numerical behavior. Here we propose an alternate approach, adapted from a paper by Bojanczyk and Steinhardt, using orthogonal transformations, which leads to more stable fast square-root algorithms. Applications to the generalized Levinson algorithm and the Chandrasekhar equations are detailed.