ON THE REPRESENTATIONS OF POLYNOMIAL-PRESERVING TRANSFINITE INTERPOLANTS FOR SIMPLEX IN R~n
关于n维单形保多项式超限插值的表示问题

In this paper, some new results about polynomial-preserving transfinite interpolation oversimplex in R~n are obtained, which include the necessary and sufficient conditions for the existen-ce of a polynomial interpolant and the minimal degree for polynomial interpolants, the repre-sentation of the interpolant, and the dimension of the interpolant space. Several applicationsof our results, such as in triangularized data interpolation and multivariate splines, are discus-sed.