摘要
In this paper, the dimensional formulae of spline spaces S_k~μ(T) for all μ≥1, h≥4μ+ 1and arbitrary triangulation T are established with the use of conformality condition of themultivariate spline, plane graph theory and method of isomorphism of linear spaces. Fora kind of triangulation T = T(μ) as arbitrary as possible, the dimensional formula ofS_k~μ(T) for all k≥μ+ 1 is given. Especially, for μ= 1 or 2 this kind of triangulation willbe very useful to the approximation problem.
In this paper, the dimensional formulae of spline spaces S_k~μ(T) for all μ≥1, h≥4μ+ 1and arbitrary triangulation T are established with the use of conformality condition of themultivariate spline, plane graph theory and method of isomorphism of linear spaces. Fora kind of triangulation T = T(μ) as arbitrary as possible, the dimensional formula ofS_k~μ(T) for all k≥μ+ 1 is given. Especially, for μ= 1 or 2 this kind of triangulation willbe very useful to the approximation problem.
基金
Project supported by the National Natural Science Foundation of China
