The Shape Parameter in the Shifted Surface Spline—An Easily Accessible Approach

Abstract

In this paper, we present an easily accessible approach to finding a suitable shape parameter in the shifted surface spline for function interpolation. We aim at helping more readers, including mathematicians and non-mathematicians, to use our method to solve practical problems. Hence, some highly complicated mathematical theorems and definitions are avoided. The major requirement, as in our previous approach, that the data points should be evenly spaced in the domain is also relaxed. This means that the data points are purely scattered without restrictions. The drawback is that the shape parameter thus obtained is not exactly the same as the theoretically predicted optimal value, which can always be achieved by using our previous rigorous approach. However, experiments show that the gap is quite small and the final interpolation errors thus obtained are satisfactory.