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Un procédé d’approximation d’une fonction convexe lipschitzienne et de ses singularités. (French) Zbl 0581.65015
Die Arbeit enthält u.a. folgende Aussagen: Sei f:\({\mathbb{R}}\to {\mathbb{R}}\) eine konvexe und lipschitzstetige Funktion; dann kann man eine Folge von Polynomen \(P_ n^ f\) mit positiven Koeffizienten konstruieren, so daß mit Zahlen C, \(C^ f\) gilt: 1. Grad \((P^ f_ n)\leq C^ f\cdot n\) für \(n\in {\mathbb{N}}\), 2. \(f(t)=Ct+\lim_{n\to \infty}\frac{1}{n}\log P_ n^ f(e^ t)\) für \(t\in {\mathbb{R}}\). Weiter: ist \(t^*\) eine Singularität von f, so ist \(e^{t^*}\) ein Häufungspunkt (in \({\mathbb{C}})\) der Wurzeln der Polynome \(P^ f_ n\). Die letzte Aussage wird durch numerische Experimente illustriert.
Reviewer: C.Geiger

MSC:
65D15 Algorithms for approximation of functions
41A30 Approximation by other special function classes
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