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Ukrainian Mathematical Journal

, Volume 57, Issue 2, pp 331–339 | Cite as

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

  • A. V. Prymak
Article
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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 s1 (s1C(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 ω5 is the modulus of smoothness of the fifth order.

Keywords

Absolute Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. V. Prymak
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

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