The shape parameter in the shifted surface spline III
This is a continuation of our study about shape parameter, based on an approach very different from that of Luh [1]and[2]. Here we adopt an error bound of convergence order O ( d ? 1 / d ) as d?0 d ? 0 , where 0<?<1 0 < ? < 1 is a constant and d  denotes essentially the fill-distance. The constant ? ? is much smaller than the one appears in Luh [1]and[2] where the error bound is O(?1/d) O ( ? 1 / d ) only. Moreover, the constant ? ? here only mildly depends on the dimension n. It means that for high-dimensional problems the criteria of choosing the shape parameter presented in this paper are much better than those of Luh [1]and[2]. The drawback is that the distribution of data points must be slightly controlled.
shape parameter shifted surface spline radial basis function interpolation problems of high-dimensions