Research on the Center Sets for Radial Basis Functions Interpolation

Radial basis functions are powerful meshfree methods for multivariate interpolation for scattered data. But both the approximation quality and stability depend on the distribution of the center set. Many methods such as so called thinning algorithm, greedy algorithm, arclength equipartition like algorithm and k-means clustering algorithm are constructed for center choosing. But all these methods are depend only on the geometry distribution while the error theory shows that the precision depends on both power function of data centers and the induced norm of the interpolated function. In this paper, an adaptive method that depends on both the fill distance and the interpolated function is recommended. On the other hand, using the RBF method directly will get a big error at the boundary of the interpolate area with a much better accuracy on the internal. Here we propose an improved RBF method by extrapolation overcome this disadvantage.