Abstract
LetW 2 n M be the class of functionsf: Δ n → ℝ (when Δ n is ann-simplex) with bounded second derivative (whose absolute value does not exceedM>0) along any direction at an arbitrary point of the simplex Δ n . LetP 1,n (f;x) be the linear polynomial interpolatingf at the vertices of the simplex. We prove that there exists a functiong ∈ W 2 n M such that for anyf ∈W 2 n M and anyx ∈ Δ n one has ¦f (x)−P 1, n (f;x)¦≤g(x).
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References
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Additional information
Translated fromMatematicheskie Zametki, Vol. 60, No. 4, pp. 504–510, October, 1996.
I thank Yu. N. Subbotin for posing the problem and for his attention to my work.
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Kilizhekov, Y.A. Approximation error for linear polynomial interpolation onn-simplices. Math Notes 60, 378–382 (1996). https://doi.org/10.1007/BF02305420
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DOI: https://doi.org/10.1007/BF02305420