2018
Том 70
№ 7

Shape-Preserving Smoothing of 3-Convex Splines of Degree 4

Prymak A. V.

Abstract

For every 3-convex piecewise-polynomial function s of degree ≤ 4 with n equidistant knots on [0, 1] we construct a 3-convex spline $s_1 (s_1 ∈ C (3))$ of degree ≤ 4 with the same knots that satisfies the inequality $$\left\| {S - S_1 } \right\|_{C_{[0,1]} } \leqslant c\omega _5 (s;1/n),$$ where $c$ is an absolute constant and $ω_5$ is the modulus of smoothness of the fifth order.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 2, pp 331-339.

Citation Example: Prymak A. V. Shape-Preserving Smoothing of 3-Convex Splines of Degree 4 // Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 277–283.

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