用广义交互确认方法选择良好参数进行多元多项式散乱数据自然样条光顺

1．简介多元样条函数在多元逼近中发挥很大作用，已有数量相当多的综合报告和研究论文正式发表，就在1996年6月在法国召开的第三届国际曲线与曲面会议上便有不少多元样条方面的报告，不过总的感觉是仍然缺乏对噪声数据特别是散乱数据的有效光顺方法．李岳生、崔锦泰、关履泰、胡日章等讨论广义调配样条与张量积函数，并用希氏空间样条方法处理多元散乱数据样条插值与光顺，提出多元多项式自然样条，推广了相应一元的结果．我们知道，在样条光顺中有一个如何选择参数的问题，用广义交互确认方法（generalizedcross－validation，以下简称GC…

MUCTIVARIATE POLYNOMIAL NATURAL SPLINE SMOOTHING OF SCATTERED DATA AND GENERALIZED CROSS-VXLIDATION FOR CHOOSING A GOOD MRAMETER

By means of the theory of spline functions in Hilbert space, multivariate polynomial natural splines smoothing of scattered data are constructed without boundary conditions on certain bounded domains in R as a generalization of the well known uniariate natural polynomial splines smoothing. Generalized Cross-validation as a useful method for choosing a good ridge parameter of these multivariate smoothing splines is discussed. We give a available algorithm. Especialy an algorithm for bicubic splines smoothing is fairly easy to implement as example, and should be very useful in multivariate numerical analysis and signal analysis.