折返插值法

Interpolation with back turn transform

现今存在许多以显式形式表示插值函数的一维插值方法。为了使这些方法能够用于解决有序数据点的插值问题,首先提出了一种有序数据点插值问题的表达形式,在这种形式中,插值函数以显式方程的形式进行表示。之后,提出了一种带数据点变换的插值思想,即通过添加数据点变换来克服传统插值方法的局限性。然后,提出了一种特殊的数据点变换--折返变换,通过添加折返变换使传统的显式方法能够用于解决有序数据点的插值问题。最后展示了两个数值算例。

Nowadays,there exist lots of one-dimensional interpolation methods whose interpolation function is expressed in explicit form.In order to make these methods solve the problem of interpolation for sequential nodes,first,an expression form of the interpolation problem for sequential nodes is presented,in which the interpolation function is expressed in explicit form.Then an idea of interpolation with node transform is proposed,which can overcome the limitation of the traditional interpolation methods by adding a node transform.After that,a special transform called Back Turn Transform is proposed.By adding the Back Turn Transform,the traditional explicit methods can be used to solve the problem of interpolation for sequential nodes.Finally,two numerical examples are demonstrated.