A constructive approach to kergin interpolation in R^k: Multivariate B-splines and lagrange interpolation

In this paper we construct an interpolation map from Cn(Rk) into 𝛑n(R(k)) (polynomials of total degree ≦ n) whose existence and uniqueness was proved by P. Kergin. We also provide numerically efficient and stable recurrence relations for computing the multivariate B-spline and its derivatives. © 1980 Rocky Mountain Journal of Mathematics.