BOOLEAN BIVARIATE LAGRANGE INTERPOLATION

In this paper the Boolean method for approximation of multivariate functions developed by Gordon [4], [5] is systematically applied to bivariate Lagrange interpolation. Interpolation methods are considered whose interpolation projectors can be characterized by K-times (K ∈ ℕ) Boolean sums of tensor product Lagrange interpolation projectors. Using certain properties of Boolean Lagrange interpolation projectors we derive explicit representation formulas for the interpolants. After showing that the classical Biermann interpolation on a triangular mesh is a special case of Boolean Lagrange interpolation a method for the construction of Serendipity elements of arbitrary order is presented. This method provides a systematic generalization of the construction of special Serendipity elements proposed by Gordon-Hall [6]. Furthermore, we derive an explicit remainder representation formula for Boolean Lagrange interpolation. Finally, a list of generalized Serendipity elements of order N-1 (2≦N≦8) is presented. © 1979 Springer-Verlag.