Aitken-Neville formulae for multivariate interpolation (Q2895245)

Aitken-Neville formulae for polynomial interpolation allow extensions of univariate polynomial approximations to several variables; this has been studied in much detail by the two current authors. In this paper they revisit their earlier work to identify important points which also stretch from the previous papers to newer approaches. Among other things, a general Aitken-Neville formula is given in two ways, Aitken-Neville sets are defined, and, further, recursion formulae, total degree polynomial interpolation and geometric characterizations of correct sets for interpolation are in special focus.