MULTIVARIATE INTERPOLATION IN ODD-DIMENSIONAL EUCLIDEAN SPACES USING MULTIQUADRICS

Let {Mathematical expression} or {Mathematical expression}. Given f:ℛn→ℛ, we establish convergence orders of interpolation where the cardinal function x with x(j)=δ0 j is a linear combination of integer shifts, of a fast decaying function {Mathematical expression}N ⊂F″being a finite subset. If n is odd and {Mathematical expression}, we find convergence orders of hn+1, whereas for {Mathematical expression}, convergence orders of hn-1 are obtained when n≥3 is odd. © 1990 Springer-Verlag New York Inc.