On $L_p$-error of bivariate polynomial interpolation on the square

Yurii Kolomoitsev; Tetiana Lomako; Jürgen Prestin

On $L_p$-error of bivariate polynomial interpolation on the square

Classical Analysis and ODEs 2017-12-19 v1

Authors: Yurii Kolomoitsev , Tetiana Lomako , Jürgen Prestin

Abstract

We obtain estimates of the $L_p$ -error of the bivariate polynomial interpolation on the Lissajous-Chebyshev node points for wide classes of functions including non-smooth functions of bounded variation in the sense of Hardy-Krause. The results show that $L_p$ -errors of polynomial interpolation on the Lissajous-Chebyshev nodes have almost the same behavior as the polynomial interpolation in the case of the tensor product Chebyshev grid.

Keywords

bivariate polynomial interpolation L_p-error Lissajous-Chebyshev nodes bounded variation Hardy-Krause tensor product Chebyshev grid

Cite

@article{arxiv.1712.06075,
  title  = {On $L_p$-error of bivariate polynomial interpolation on the square},
  author = {Yurii Kolomoitsev and Tetiana Lomako and Jürgen Prestin},
  journal= {arXiv preprint arXiv:1712.06075},
  year   = {2017}
}

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