Abstract
It is well known that the nonlinear problem of interpolatingm+n+1 data by a rational function of type (m, n) may have no solution, but that the corresponding linearized problem (obtained by multiplying through by the denominator) always leads to a unique rational function, which is often still called the rational interpolant. For fixedm andn, and fixed (possibly multiple) interpolation points, the dependence of this interpolant on the prescribed function values is studied here. For ten notions of convergence in the spaceℛ m, n the question of the continuity of this interpolation operator is investigated.
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Communicated by William B. Gragg.AMS classification: 41A24, 30E05, 41A20, 65D05.
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Gutknecht, M.H. In what sense is the rational interpolation problem well posed. Constr. Approx 6, 437–450 (1990). https://doi.org/10.1007/BF01888274
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DOI: https://doi.org/10.1007/BF01888274