Abstract
We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [−π, π]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.
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Communicated by C. Brezinski
This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.
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Bultheel, A., González-Vera, P., Hendriksen, E. et al. On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle. Numer Algor 13, 321–344 (1996). https://doi.org/10.1007/BF02207699
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DOI: https://doi.org/10.1007/BF02207699