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The Quasi-Interpolant as a Tool in Elementary Polynomial Spline Theory

By Carl de Boor

Abstract

ll of the t j 's coincide. I leave unresolved any possible ambiguity when t = t j for some j, and concern myself only with left and right limits at such a point; i.e., I replace each t = t j by the "two points" t - j and t + j . As is well known, N ik > 0 on (t i , t i+k ), and N ik = 0 o# [t + i , t - i+k ] so that (since t i < t i+k , by assumption) N ik is not identically zero, while on the other hand, no more than k of the N jk 's are nonzero at any particular point. Consequently, for an arbitrary a #<F

Year: 1973
OAI identifier: oai:CiteSeerX.psu:10.1.1.25.2992
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