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计算数学  1993 

TWO-STAGE SPLINE METHOD AND ITS ERROR BOUND FOR THE SCATTERED DATA IN R~2
多元散乱数据二步拟合法及其误差估计

Keywords: 散乱数据,曲面拟合,误差估计

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Abstract:

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.

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