Abstract
Let the spline functionS m of degree 2m−1 and period 1 be the unique solution of the interpolation problem in § 1. An interesting question was posed by Schoenberg [1], p. 125: What happens toS m if we letm→∞? In this paper, we prove that the spline functionsS m and their derivatives converge form→∞ to a well determined trigonometric polynomial and its derivatives. Estimates for the rate of convergence are given.
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v. Golitschek, M. On the convergence of interpolating periodic spline functions of high degree. Numer. Math. 19, 146–154 (1972). https://doi.org/10.1007/BF01402525
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DOI: https://doi.org/10.1007/BF01402525