Scattered Data Interpolation Methods And Its Applications

This paper mainly introduces two kinds of scattered data interpolation methods, they are Radial basis function method and Kriging method. The ap-plication of radial basis function method in inverse problem of one dimensional heat equation is studied, numerical methods and the numerical test for solving this kind of problem are given, and discusses the effects of noise disturbance and free parameters on the numerical results. Numerical experiments show that approximation error decreases with the decrease of the time step and decreases with the increase the number of nodes. Both in uniform collocation and in non uniform collocation, radial basis function method is better than finite difference method. In the presence of noise disturbance, error decreases with the decrease of noise reducing; Kriging method is used to analysis spatial-temporal variation of groundwater and the characteristic of its distribution in Cele Oasis, the results show that Gauss model is the best model in the analyzing of groundwater change, spatial heterogeneity and connectivity of groundwater depth are enhanced, the groundwater depth in the southern part of Cele oasis is larger than that in other regions.