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Numerical Algorithms

, Volume 70, Issue 2, pp 249–267 | Cite as

Reusing Chebyshev points for polynomial interpolation

  • Saman GhiliEmail author
  • Gianluca Iaccarino
Original Paper

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.

Keywords

Polynomial interpolation Chebyshev points Lebesgue constant 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA
  2. 2.Department of Mechanical Engineering and Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA

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