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A Voronovskaya Theorem for Variation-Diminishing Spline Approximation
Published online by Cambridge University Press: 20 November 2018
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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 ≧ xi + 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 ΣjNj(x) = 1. See, e.g., [2] for a precise definition of the Nj(x) and a discussion of the properties of Vf.
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- Copyright © Canadian Mathematical Society 1986
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