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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Splines with nonnegative $B$-spline coefficients

Authors: C. de Boor and James W. Daniel
Journal: Math. Comp. 28 (1974), 565-568
MSC: Primary 65D15
MathSciNet review: 0378357
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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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Keywords: Nonnegative splines, one-sided approximation, splines, approximation
Article copyright: © Copyright 1974 American Mathematical Society