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
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.
