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

• Datum: 2005
• Hauptverfasser: Prymak, A. V., Примак, А. В.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2005
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3596
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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 $c$...