By means of the theory of spline functions in Hilbert space, multivariate polynomial natural splines smoothing of scattered data are constructed without boundary conditions on certain bounded domains in R as a general...By means of the theory of spline functions in Hilbert space, multivariate polynomial natural splines smoothing of scattered data are constructed without boundary conditions on certain bounded domains in R as a generalization of the well known uniariate natural polynomial splines smoothing. Generalized Cross-validation as a useful method for choosing a good ridge parameter of these multivariate smoothing splines is discussed. We give a available algorithm. Especialy an algorithm for bicubic splines smoothing is fairly easy to implement as example, and should be very useful in multivariate numerical analysis and signal analysis.展开更多
In this paper, the dimension formulaes of multivariate weak spline are discussed. The dimension formulaes of non-degree multivariate weak spline on a vertex are presented. The dimension formulaes on triangulation are ...In this paper, the dimension formulaes of multivariate weak spline are discussed. The dimension formulaes of non-degree multivariate weak spline on a vertex are presented. The dimension formulaes on triangulation are also discussed. At last, the local supported bases of W31(I1Δ) are presented.展开更多
In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piec...In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piecewise algebraic sets, and turn theisomorphism and classifying problem of piecewise algebraic sets into the isonorphismand classifying problem of commutative algebras.展开更多
文摘By means of the theory of spline functions in Hilbert space, multivariate polynomial natural splines smoothing of scattered data are constructed without boundary conditions on certain bounded domains in R as a generalization of the well known uniariate natural polynomial splines smoothing. Generalized Cross-validation as a useful method for choosing a good ridge parameter of these multivariate smoothing splines is discussed. We give a available algorithm. Especialy an algorithm for bicubic splines smoothing is fairly easy to implement as example, and should be very useful in multivariate numerical analysis and signal analysis.
基金Project supported by the National Natural Science Foundation of China (19871010, 69973010)
文摘In this paper, the dimension formulaes of multivariate weak spline are discussed. The dimension formulaes of non-degree multivariate weak spline on a vertex are presented. The dimension formulaes on triangulation are also discussed. At last, the local supported bases of W31(I1Δ) are presented.
文摘In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piecewise algebraic sets, and turn theisomorphism and classifying problem of piecewise algebraic sets into the isonorphismand classifying problem of commutative algebras.
