# zbMATH — the first resource for mathematics

The non-Sibsonian interpolation: A new method of interpolation of the value of a function on an arbitrary set of points. (English. Russian original) Zbl 0948.65005
Comput. Math. Math. Phys. 37, No. 1, 9-15 (1997); translation from Zh. Vychisl. Mat. Mat. Fiz. 37, No. 1, 11-17 (1997).
The authors propose an interpolation algorithm which is a new method for interpolating the value of a function on a set of arbitrary points in a finite-dimensional Euclidean space $$E_n$$. The proposed algorithm calculates the value $$f_0$$ of a scalar function $$f(x)$$ of a prescribed point $$x_0$$ in $$E_n$$, given its values $$\{f_k\}$$ on fixed system points (nodes) $$\{x_k\}$$ in $$E_n$$. The point to which the values of $$f$$ are interpolated is supposed to be inside the domain bounded by a convex hull constructed on the basis of points $$\{x_k\}$$. In contrast to the method of R. A. Sibson [Math. Proc. Camb. Philos. Soc. 87, 151–155 (1980; Zbl 0466.52010)], the interpolation proposed is easier and more efficient.

##### MSC:
 65D05 Numerical interpolation 41A05 Interpolation in approximation theory