Conditions And Interpolation Of Multivariate Spline Space Singularity 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. From this, by discussing the singularity of this space, get the general algebraic condition when this space is singularity. Finally, two kinds of applied geometry distinguishing condition are given when this spline space is singularity.2. Discuss the Interpolation properly posed problem of I type partition in S\space, and give two examples.3. By applying the algorithm 1,prove the lemma in literature [1],...