Abstract
A famous unsolved problem in the theory of polynomial interpolation is that of explicitly determining a set of nodes which is optimal in the sense that it leads to minimal Lebesgue constants. In [11] a solution to this problem was presented for the first non-trivial case of cubic interpolation. We add here that the quantities that characterize optimal cubic interpolation (in particular: the minimal Lebesgue constant) can be compactly expressed as real roots of certain cubic polynomials with integral coefficients. This facilitates the presentation and impartation of the subject matter and may guide extensions to optimal higher-degree interpolation.
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Rack, HJ. (2013). An Example of Optimal Nodes for Interpolation Revisited. In: Anastassiou, G., Duman, O. (eds) Advances in Applied Mathematics and Approximation Theory. Springer Proceedings in Mathematics & Statistics, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6393-1_7
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DOI: https://doi.org/10.1007/978-1-4614-6393-1_7
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