关于一类Radial Basis插值的收敛性分析

ON THE CONVERGENCE ANALYSIS FOR A CLASS OF RADIAL BASIS INTERPOLATION

Radial Basis插值是一种适用于多变量散乱数据的插值方法,有着广泛的应用.本文对函数f分析了用Hardy的inverse multiquadric进行Radial Basis插值当结点密集时的收敛阶.并找到了一族函数.对它们进行Radial Basis插值是连同各阶导数一致收敛的。

Radial Basis interpolation is a suitable method for multivariate scattered data interpolation. It is widely used in application. Let(r) = 1/(c + r2)·β Given f: R→R , we establish convergence orders for Radial Basis interpolation with Hardy's inverse multiquadricHf = Σλj(x - ri)with Hf(xi) = f(xi) , as {xi} becomes dense in some region Ω We find a class of founctions,that Hf is uniformly convergent to f as well as its all order of derivatives.