Aitken-Neville sets, principal lattices and divided differences
The multivariate polynomial interpolation is related to generalized principal lattices. It is shown that any generalized principal lattice is an Aitken-Neville configuration (and so can be evaluated by iterated linear interpolation). The converse will be shown for dimension 2 and \(dg\geq3\). The divided differences, associated to Aitken-Neville configuration are considered and their spline representation is derived.
scientific article; zbMATH DE number 5534943