Some Triangulation Spline Function Space Singularity And Interpolation Posedness

Because the structure of multivariate spline space not only depends on the topology character of partition, but only the geometry character of partition, some multivariate spline spaces are singularity. This paper proceed from conformality equation, apply generator basis algorithm of module in ring of polynomial, calculate out smoothing cofactor of similar Morgan-scott partition space in Mathematica software environment. The main work of this thesis can be summarized as follows:1. We obtain the sufficient and necessary condition in algebraical formwhen the multivariate spline space S₄²(△_MS)is singular, and give thecorreponding dimension.2. A constructive method is presented for Lagrange interpolation set in and some corresponding examples are given.