(untitled) (Journal of Computational Mathematics, 2001)
A general local C^m (m 0) tetrahedral interpolation scheme by polynomials of degree 4m+1 plus low order rational functions from the given data is proposed. The scheme can have either 4m+1 order algebraic precision if C^2m data at vertices and C^m data on faces are given or k+E[k/3]+1 order algebraic precision if C^k (k 2m) data are given at vertices. The resulted interpolant and its partial derivatives of up to order m are polynomials on the boundaries of the tetrahedra.