多元散乱数据二步拟合法及其误差估计

多元数据曲面拟合的早期结果,主要在研究格子点的插值问题上,其方法是张量积插值或利用再生核希氏空间理论给出解的构造。1]系统地总结了1976年以前的研究概况,2]则为全平面上的薄板样条是一元样条到多元样条非张量积形式的推广。它是基于再生核的明显表示,但对一般的泛函来说,要得到再生核通常是很困难的。最近,4]避开这一实质性困难,利用Lagrange恒等式,Euler方程及最优插值的特征定理给出了一

TWO-STAGE SPLINE METHOD AND ITS ERROR BOUND FOR THE SCATTERED DATA IN R~2

In this paper, a kind of two-stage spline method for fitting surfaces to scattered data is pre-sented. Compared with some existing methods, such as thin plate spline, radial function me-thod and the multivariate smoothing interpolation etc, where the coefficient matrices associatedwith these methods are not sparse, when number of interpolation points N is very large, the timeand storage of computing will increase rapidly and the coefficient matrices may become ill-conditioned, this method can be carried out only by solving some linear algrebraic systems withbandwidth coefficient matrices. So we can save the storage of computing, eliminate the illnessof matrices and reduce the time of computation greatly. Error bound of two-stage method isalso given. Finally, some numerical examples are presented, and the computing results finelycoincide with the exact values of given functions.