Remarks on a unified theory for classical and generalized interpolation and extrapolation

A unified theory for generalized interpolation, as developed by Mühlbach, and classical polynomial interpolation is discussed. A fundamental theorem for generalized linear iterative interpolation is given and used to derive generalizations of the classical formulae due to Neville, Aitken and Lagrange. Using Mühlbach's definition of generalized divided differences, Newton's generalized interpolation formula, including an expression for the error term, is derived as a pure identity.