Abstract
We generalize to the Canonical Complete Chebyshev splines some properties already known for Extended Chebyshev and piecewise Extended Chebyshev splines, like Marsden identity and Greville points. Also, we represent an interesting algorithm which leads to numerically stable expressions for the Greville points for CCC-splines. We show that any CCC-spline space provides us with infinite number of operators of the Schoenberg-type, and we give a simple characterization of them. After proving few important properties, we establish a sufficient condition for quadratic convergence of approximations by CCC-Schoenberg operators to a given function.
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This research was supported by Ministry of science, education and sports of the Republic of Croatia under Grant 037-1193086-2771.
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This article is in memory and honor of Mladen Rogina who passed away on 24 January 2013, as our last joint work.
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Bosner, T., Rogina, M. Quadratic convergence of approximations by CCC-Schoenberg operators. Numer. Math. 135, 1253–1287 (2017). https://doi.org/10.1007/s00211-016-0831-0
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DOI: https://doi.org/10.1007/s00211-016-0831-0