The non-Sibsonian interpolation: A new method of interpolation of the value of a function on an arbitrary set of points (Q1974717)

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 \textit{R. A. Sibson} [Math. Proc. Camb. Philos. Soc. 87, 151--155 (1980; Zbl 0466.52010)], the interpolation proposed is easier and more efficient.