Splines with nonnegative 𝐵-spline coefficients

de Boor, C.; Daniel, James W.

doi:10.1090/S0025-5718-1974-0378357-2

Splines with nonnegative $B$-spline coefficients
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by C. de Boor and James W. Daniel PDF

Math. Comp. 28 (1974), 565-568 Request permission

Abstract:

We consider the question of the approximation of nonnegative functions by nonnegative splines of order k (degree $< k$) compared with approximation by that subclass of nonnegative splines of order k consisting of all those whose B-spline coefficients are nonnegative; while approximation by the former gives errors of order ${h^k}$, the latter may yield only ${h^2}$. These results are related to certain facts about quasi-interpolants.

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