Key points are not available for this paper at this time.
Given any data points xl, . . ., x,, in RW and values f(x)... f(x) of a function f, Shepard's global interpolation formula reads as follows: Sof (x) =Ef (xi) Wi (X, Wi (X = I X Xi I -P/ElX xjl |P. where | I denotes the Euclidean norm in WR. This interpolation scheme is stable, but if p > 1, the gradient of the interpolating function vanishes in all data points. The interpolation operator Spq is defined by replacing the values f(xi) in Spf by Taylor polynomials of f of degree q E= N. In this paper, we investigate the approximating power of Spq for all values of p, q and s.
Reinhard Farwig (Tue,) studied this question.