多元再生核径向基函数研究

Study of Multivariate Reproducing Kernel Radial Basis Function

通过研究多元再生核函数插值,发现再生核函数是一个径向基函数,在对再生核函数进行多元插值的时候,可以直接进行径向基插值,而不必像以往一样只能进行张量积展开.径向基插值方法简单,易于计算机实现,计算精度高.通过数值实验,直接进行插值比张量积精度要高,同时在与其他多元函数插值进行比较后,获得了理想的结果.

By studying the multivariate reproducing kernel function interpolation, it is found that the reprodu- cing kernel function itself is also a radial basis function. When the multivariate reproducing kernel function is interpolated, direct interpolate can be conducted rather than using its tensor product. This method is simple, easy to implement with high accuracy compared with direct tensor product interpolation by numerical experi- ments to gain more desired results than other multivariate function interpolation.