Some Local Methods for Scattered Data Interpolation

Abstract:

      With regard to the Shepard method, in this paper, we use the truncated polynomial, the B-spline basis function and exponential function to construct the weight functions. They are of better property of smoothness and decay, which can be adjusted freely. And so the surface can be fitted better by the improved method. we also present a new local method, which performs better than the local Shepard method does. Moreover, we use the idea of multivariate spline to give out two local methods of the multiquadric interpolation. These methods perform almost as good as the global multiquard method does.