Abstract
Lets be a cubic spline, with equally spaced knots on [a, b] interpolating a given functiony at the knots. The parameters which determines are used to construct a piecewise defined polynomialP of degree four. It is shown thatP can be used to give better orders of approximation toy and its derivatives than those obtained froms. It is also shown that the known superconvergence properties of the derivatives ofs, at specific points of [a, b], are all special cases of the main result contained in the present paper.
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Behforooz, G.H., Papamichael, N. Improved orders of approximation derived from interpolatory cubic splines. BIT 19, 19–26 (1979). https://doi.org/10.1007/BF01931217
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DOI: https://doi.org/10.1007/BF01931217