Practical, Reliable, Rational Interpolation

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Abstract
An algorithm incorporating features essential for practical, reliable, rational interpolation is explained. This algorithm generates a Thiele-Werner continued fraction representation of the interpolant. A backward error analysis is presented for the algorithm, as well as for its special cases of Newton polynomial interpolation and Thiele rational interpolation. This is made possible by introducing into the Newton method, Thiele method and Werner method a strategy for selecting the interpolation points in an optimal order.

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