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Upper Bound for Lebesgue Constant of Bivariate Lagrange Interpolation Polynomial on the Second Kind Chebyshev Points

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  • Juan Liu
  • Laiyi Zhu
  • Efthymios G. Tsionas

Abstract

In the paper, we study the upper bound estimation of the Lebesgue constant of the bivariate Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the second kind on the square −1,12. And, we prove that the growth order of the Lebesgue constant is On+22. This result is different from the Lebesgue constant of Lagrange interpolation polynomial on the unit disk, the growth order of which is On. And, it is different from the Lebesgue constant of the Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the first kind on the square −1,12, the growth order of which is Olnn2.

Suggested Citation

  • Juan Liu & Laiyi Zhu & Efthymios G. Tsionas, 2021. "Upper Bound for Lebesgue Constant of Bivariate Lagrange Interpolation Polynomial on the Second Kind Chebyshev Points," Journal of Mathematics, Hindawi, vol. 2021, pages 1-19, December.
    • Handle: RePEc:hin:jjmath:5649969
    DOI: 10.1155/2021/5649969
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