Reusing Chebyshev points for polynomial interpolation (original) (raw)

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_=2_m 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_≠2_m 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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Authors and Affiliations

  1. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
    Saman Ghili
  2. Department of Mechanical Engineering and Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
    Gianluca Iaccarino

Authors

  1. Saman Ghili
  2. Gianluca Iaccarino

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Correspondence toSaman Ghili.

Additional information

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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