薄板样条函数逐次增加节点的算法

Stepwise algorithm of thin plate splines

薄板样条是一种可以推广到在多维空间的插值方法,在测绘与其它众多学科中都有重要的应用。根据实际需要提出了一种逐次增加节点的插值算法。这种算法使用分块求逆技术,可以降低整体计算的求逆的阶数,也可以按给定的精度最佳的选择节点。

Thin plate splines, as an interpolating method which can be generalized to multidimensional space, is useful in surveying and mapping and many other subjects. According to the application it gives an algorithm adding nodes step by step to get thin plate splines. By using the technique of inverse matrix partly, this method can reduce the workload of calculation and can give the best choice of the least amount nodes on the request of precision.