Abstract
This paper is concerned with the problem of approximating functions in the L1-norm by spline functions with fixed and free knots and its applications to the approximation of linear functionals. For this best L1-approximation characterizations are given which involve perfect splines. In addition, one-sided approximation is studied in more detail. The results are used to give another proof of the existence of a monospline with maximal number of zeros.
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Strauß, H. (1976). Approximation mit splinefunktionen und quadraturformeln. In: Böhmer, K., Meinardus, G., Schempp, W. (eds) Spline Functions. Lecture Notes in Mathematics, vol 501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079756
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DOI: https://doi.org/10.1007/BFb0079756
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