Improved orders of approximation derived from interpolatory cubic splines
Date
1979Author
Behforooz, G. H.Papamichael, Nicolas
Source
BITVolume
19Issue
1Pages
19-26Google Scholar check
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Let s be a cubic spline, with equally spaced knots on [a, b] interpolating a given function y at the knots. The parameters which determine s are used to construct a piecewise defined polynomial P of degree four. It is shown that P can be used to give better orders of approximation to y and its derivatives than those obtained from s. It is also shown that the known superconvergence properties of the derivatives of s, at specific points of [a, b], are all special cases of the main result contained in the present paper. © 1979 BIT Foundations.