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In [2] we used rational functions with a fixed denominator, i.e., independent of the interpolated function, to construct interpolating linear projections with slowly increasing Lebesgue constants for arbitrary interpolation points. Their drawback was the relatively slow convergence of the interpolant as the number of points increases. In the present work, we demonstrate how the convergence can be dramatically improved by limiting the degree of the denominator.

Exponentially convergent linear rational interpolation between equidistant (and other) points