Geodesic
A Voronovskaya Theorem for Variation-Diminishing Spline Approximation
Canadian journal of mathematics, Tome 38 (1986) no. 5, pp. 1081-1093

Voir la notice de l'article provenant de la source Cambridge University Press

In [7] Schoenberg introduced the following variation-diminishing spline approximation methods.Let m > 1 be an integer and let Δ = {xi } be a biinfinite sequence of real numbers with xi ≧ x i + l < xi+m . To a function f associate the spline function Vf of order m with knots Δ defined by (1.1) where and the Nj(x) are B-splines with support xj < x < xj+m normalized so that Σj Nj(x) = 1. See, e.g., [2] for a precise definition of the Nj(x) and a discussion of the properties of Vf. 
Marsden, M. J. A Voronovskaya Theorem for Variation-Diminishing Spline Approximation. Canadian journal of mathematics, Tome 38 (1986) no. 5, pp. 1081-1093. doi: 10.4153/CJM-1986-053-0
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[1] 1. Bajsanski, B. and Bojanic, R., A note on approximation by Bernstein polynomials, Bull. Am. Math. Soc. 70 (1964), 675–677. Google Scholar

[2] 2. de Boor, C., A practical guide to splines, Applied Math. Sciences 27 (Springer-Verlag, New York, 1978). Google Scholar | DOI

[3] 3. DeVore, R., The approximation of continuous functions by positive linear operators, Lecture Notes in Mathematics 293 (Springer-Verlag, Berlin, 1972). Google Scholar | DOI

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[7] 7. Schoenberg, I. J., On spline functions, In Inequalities (Academic Press, New York, 1967), 255–291. Google Scholar

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