Abstract
Let \({X_{l}^{C}}\) be the set of l Chebyshev points in the interval [−1,1]. If n and n 0 are such that n=2m n 0−1 for some positive integer m, then \(X_{n_{0}}^{C} \subset {X_{n}^{C}}\). This property can be utilized in order to reuse previous function values when one wants to increase the degree of the polynomial interpolation. For given n 0 and n, n>n 0, where n≠2m n 0−1, we give a simple procedure to build a set of n points in the interval [−1,1] that include the set of n 0 Chebyshev points and have favorable interpolation properties. We show that the nodal polynomial for these points has a maximum norm that is at most O(n) times larger than that of the Chebyshev points of the same size. We also present numerical evidence suggesting that the Lebesgue constant for these points grows at most linearly in n.
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This work is supported by the PECASE Award, sponsored by the Lawrence Livermore National Laboratory under grant B597952 and the Office of Science of the U.S. Department of Energy under grant DE-SC0005384.
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Ghili, S., Iaccarino, G. Reusing Chebyshev points for polynomial interpolation. Numer Algor 70, 249–267 (2015). https://doi.org/10.1007/s11075-014-9945-6
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DOI: https://doi.org/10.1007/s11075-014-9945-6