Abstract
This paper is concerned with the construction of the fundamental functions associated with a two-point Hermite spline interpolation scheme used by Martensen in the context of the remainder of the Gregory quadrature rule. We derive both a recursive construction and an explicit representation in terms of the underlying B-Splines which can easily be deduced using Marsden’s identity. We can make use of these functions in order to introduce a local interpolation scheme which reproduces all splines. Finally, we examine the error of this interpolant to a sufficiently smooth function and realize that it behaves like \(\mathcal{O}(h^{n+1})\) in the case of splines of degree n.
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AMS subject classification (2000)
65D05, 65D07, 41A15
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Siewer, R. Martensen Splines. Bit Numer Math 46, 127–140 (2006). https://doi.org/10.1007/s10543-006-0048-1
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DOI: https://doi.org/10.1007/s10543-006-0048-1