On L_p-error of bivariate polynomial interpolation on the square

2017/12/17 by Yurii Kolomoitsev, Kolomoitsev, Yurii, Tetiana Lomako +3
Mathematics · #41A05 #41A25 #42A15 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1712.06075

openalex publication_date 2017/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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