Numerical Analysis Using Sage pp 227-261 | Cite as
Spline Interpolation
Chapter
Abstract
Given the set of n + 1 data points, we have seen how we can obtain a polynomial function of degree (at most) n, \(p(x) = a_{n}x^{n} + a_{n-1}x^{n-1} + \cdots + a_{1}x + a_{0}\) that interpolates these points. That is: This, however, has a major drawback: the polynomial can have a very high degree (up to n) and hence, the interpolating function can oscillate too much. The oscillation may be quite wild even when all the y-values of the data set given are essentially constant.
$$\displaystyle{ \begin{array}{l|l|l|l|l} x_{0} & x_{1} & x_{2} & \ldots & x_{n} \\ \hline y_{0} & y_{1} & y_{0} & \ldots & y_{n} \end{array},\text{ with }x_{0} < x_{1} < \cdots < x_{n}, }$$
$$\displaystyle{ p(x_{0}) = y_{0},p(x_{1}) = y_{1},\ldots,p(x_{n}) = y_{n}. }$$
Supplementary material
References
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