On bivariate osculatory interpolation

Abstract In this paper the straight-line-superposed interpolation which was first proposed by Liang (1965) for the bivariate Lagrange interpolation problem is generalized to set up a new bivariate interpolation method, the order-raising process. The new method expands and develops the bivariate osculatory interpolation schemes proposed by Le Mehaute (1981) and Hakopian (1984).