Abstract
This paper gives a review of univariate splines and B-splines, with special emphasis on total positivity. In particular, we show that the B-spline basis is totally positive, and we give a proof of the SchoenbergWhitney theorem by first establishing the result for the so-called truncated power basis. One consequence of total positivity is the existence of the Chebyshev spline which is a generalization of the Chebyshev polynomial. This spline has many nice properties, and we study some of these at the end of the paper.
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Mørken, K. (1996). Total Positivity and Splines. In: Gasca, M., Micchelli, C.A. (eds) Total Positivity and Its Applications. Mathematics and Its Applications, vol 359. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8674-0_3
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DOI: https://doi.org/10.1007/978-94-015-8674-0_3
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