The quasi–interpolant as a tool in elementary polynomial spline theory
نویسنده
چکیده
taking, for each fixed t, the k divided difference of g(s) := gk(s; t) at ti, . . . ti+k in the usual manner even when some or all of the tj ’s coincide. I leave unresolved any possible ambiguity when t = tj for some j, and concern myself only with left and right limits at such a point; i.e., I replace each t = tj by the “two points” tj and t + j . As is well known, Nik > 0 on (ti, ti+k), and Nik = 0 off [t+i , t − i+k] so that (since ti < ti+k, by assumption) Nik is not identically zero, while on the other hand, no more than k of the Njk’s are nonzero at any particular point. Consequently, for an arbitrary a ∈ IR, the rule
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