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On a conjecture of Carl de Boor regarding the limits of Lagrange interpolants. (English) Zbl 1239.41008
Summary: The purpose of this paper is to provide a counterexample to a conjecture of C. de Boor [Approximation Theory XI: Gatlinburg 2004, Nashboro Press, 59–91 (2005; Zbl 1126.41003)], that every ideal projector is a limit of Lagrange projectors. The counterexample is based on a construction of A. Iarrobino [in: Algebraic geometry, Proc. Summer Res. Inst., Brunswick/Maine 1985, part 2, Proc. Symp. Pure Math. 46, 297–320 (1987; Zbl 0646.14002)] pointed to in this context by G. Ellingsrud (as mentioned in de Boor’s paper [loc. cit.]). We also show that the conjecture is true for polynomials in two variables.

##### MSC:
 41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX) 41A05 Interpolation in approximation theory 65D05 Numerical interpolation
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