Description: In this paper two theorems concerning the optimality of the perfect-fit and perfect-smoothness graduations are proved. Two examples are presented and some difficulties with regard to computational feasibility are reviewed. A discussion of the paper follows. From Transactions of Society of Actuaries 1978, Vol. 30.

Description: The primary objective of the paper was to develop a straightforward method for constructing an interpolation formula of finite range with desired properties stipulated in advance. This paper had in view mainly the application to polynomial interpolation as used in actuarial work. Followed by 2 discussion papers submitted