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第一章插值法(续) §4 逐步播值法和插值误差的事后估计拉格朗日插值公式形式简单,便于计算机计算,但要改变插值的阶数(增加结点数)就要重新计算所有系数。逐步插值法是先用少数几个结点作低阶插值,如果不能满足精度要求时,就逐步增加结点。但又不像拉格朗日插值那样重新计算所有系数。为了描述这种插值方法,引进专用符号f_k(x_i)。它表示由结点x_0,x_1,……x_(k-1)和x_i构成的K阶插值多项式,其中i≥k。即除按顺序排列的k个结点x_0,x_1……x_(k-1)之外再加一个结点x_(io)f_k(x_i)是与插值阶数k和结点x_i有关的函数。利用这一符号把x_0和x_1为结
Chapter 4 Interpolation (cont’d) §4 Postmortem Estimation of Gravimetric Methods and Interpolation Errors Lagrange interpolation formulas are simple in form and easy to use in computer calculations. However, changing the order of interpolation (increasing the number of nodes) will recalculate all coefficient. Step by step interpolation method is to first use a few nodes for low-order interpolation, if you can not meet the accuracy requirements, gradually increase the node. But not recalculating all the coefficients like Lagrange interpolation. In order to describe this interpolation method, a special symbol f_k (x_i) is introduced. It represents a K-th order interpolation polynomial formed by nodes x_0, x_1, ... x_ (k-1) and x_i, where i ≧ k. That is, a node x_ (io) f_k (x_i) is added to the interpolation order k and the node x_i in addition to the k nodes x_0, x_1, ..., x_ (k-1) arranged in order. Use this notation to concatenate x_0 and x_1