Dimension Series and Basis Function of Multivariate Spline Space

Abstract:

      For a polyhedral subdivision of region in Euclidean d-space, we consider the problem of determining the dimension and a basis for this space, give a computational scheme for obtaining the formal power series and basis of the space. Underlying this scheme is the Gr?bner basis algorithm of computational commutative algebra and coordinate factor methods. Some algorithms were given for computing the dimension series and basis for different order spline.