On Lp-error of bivariate polynomial interpolation on the square

Yurii Kolomoitsev; Tetiana Lomako; Jürgen Prestin

doi:10.1016/j.jat.2018.02.005

On L_p-error of bivariate polynomial interpolation on the square

Yurii Kolomoitsev^*, Tetiana Lomako, Jürgen Prestin

^*Corresponding author for this work

Institute of Mathematics

5 Citations (Scopus)

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.

Original language	English
Journal	Journal of Approximation Theory
Volume	229
Pages (from-to)	13-35
Number of pages	23
ISSN	0021-9045
DOIs	https://doi.org/10.1016/j.jat.2018.02.005
Publication status	Published - 01.05.2018

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10.1016/j.jat.2018.02.005

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title = "On Lp-error of bivariate polynomial interpolation on the square",

abstract = "We obtain estimates of the Lp-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 Lp-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.",

author = "Yurii Kolomoitsev and Tetiana Lomako and J{\"u}rgen Prestin",

year = "2018",

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doi = "10.1016/j.jat.2018.02.005",

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T1 - On Lp-error of bivariate polynomial interpolation on the square

AU - Kolomoitsev, Yurii

AU - Lomako, Tetiana

AU - Prestin, Jürgen

PY - 2018/5/1

Y1 - 2018/5/1

N2 - We obtain estimates of the Lp-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 Lp-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.

AB - We obtain estimates of the Lp-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 Lp-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.

UR - https://www.scopus.com/pages/publications/85043380906

U2 - 10.1016/j.jat.2018.02.005

DO - 10.1016/j.jat.2018.02.005

M3 - Journal articles

AN - SCOPUS:85043380906

SN - 0021-9045

VL - 229

SP - 13

EP - 35

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

ER -

On L_p-error of bivariate polynomial interpolation on the square

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