Abstract
It is shown that for given monotone interpolation data the function z which minimizes the Sobolew-seminorm ∣z∣2 2 = ∫ (D2 z(x))2dx among all monotone interpolating functions is a cubic spline. A sharp upper bound for the number of knots of that spline is given.
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Hornung, U. (1978). Monotone Spline-Interpolation. In: Collatz, L., Meinardus, G., Werner, H. (eds) Numerische Methoden der Approximationstheorie. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 42. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6460-2_11
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DOI: https://doi.org/10.1007/978-3-0348-6460-2_11
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-1025-7
Online ISBN: 978-3-0348-6460-2
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