Summary. A method for the construction of a set of data of interpolation in several variables is given. The resulting data, which are either function values or directional derivatives values, give rise to a space of polynomials, in such a way that unisolvence is guaranteed. The interpolating polynomial is calculated using a procedure which generalizes the Newton divided differences formula for a single variable.
Subject Classifications: AMS (MOS): 65D05, 41 A05, 41 A63.
IntroductionFor simplicity, we make our presentation for R 2 first, and then we consider higher dimensions.We choose a set of straight lines r i in R 2, each of which is associated with a polynomial of first degree in x and y, also denoted by ri. With each line r~ we consider a set of straight lines r u, in such a way that the intersections determined by r u in r i are the points at which the interpolation data will be given. The lines ri and/or r u may appear with multiplicity greater than one, leading to derivative values as interpolation data. For example, in Fig. la the data of the associated interpolation problem are f(Uoo ), f (UoO, f(uo2 ) but when u01 tends to u00 we get the situation of
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