Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials

@article{Wang2014ExplicitBW,
  title={Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials},
  author={Haiyong Wang and Daan Huybrechs and Stefan Vandewalle},
  journal={Math. Comput.},
  year={2014},
  volume={83},
  pages={2893-2914}
}
  • Haiyong Wang, Daan Huybrechs, Stefan Vandewalle
  • Published in Math. Comput. 2014
  • Mathematics, Computer Science
  • Barycentric interpolation is arguably the method of choice for numerical polynomial interpolation. In this paper we show that barycentric weights for the roots or extrema of classical families of orthogonal polynomials are expressible explicitly in terms of the nodes and weights of the corresponding Gaussian quadrature rule. Based on the Glaser-Liu-Rokhlin algorithm for Gaussian quadrature, this leads to an O(n) computational scheme for computing barycentric weights. For the Jacobi case, known… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 51 REFERENCES

    Fast and Accurate Computation of Gauss-Legendre and Gauss-Jacobi Quadrature Nodes and Weights

    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    Chebfun and numerical quadrature

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Essentials of Numerical Analysis

    VIEW 1 EXCERPT
    HIGHLY INFLUENTIAL

    Lagrangian interpolation at the Chebyshev points xn

    VIEW 3 EXCERPTS
    HIGHLY INFLUENTIAL

    Approximation Theory and Approximation Practice

    • L. N. Trefethen
    • SIAM, Philadelphia
    • 2012
    VIEW 2 EXCERPTS

    Stability of Barycentric Interpolation Formulas for Extrapolation

    VIEW 1 EXCERPT

    Trefethen , Chebfun and numerical quadrature

    • Nicholas Hale, N Lloyd
    • Sci . China Math .
    • 2012