Abstract
The solution of the trigonometric moment problem involves the computation of a (0/n) Laurent-Padé approximant for a positive real function on the complex unit circle. The incoming scheme is equivalent with the recursion for Szegö's orthogonal polynomials, while the outgoing scheme is equivalent to the schur recursion for contractions of the unit disc. The numerical stability of both algorithms is proved under certain conditions via a backward error analysis.
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Bultheel, A., Leuven, K.U. (1981). Error analysis of incoming and outgoing schemes for the trigonometric moment problem. In: de Bruin, M.G., van Rossum, H. (eds) Padé Approximation and its Applications Amsterdam 1980. Lecture Notes in Mathematics, vol 888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095579
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DOI: https://doi.org/10.1007/BFb0095579
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