保驻点曲线插值
首发时间:2012-03-28
摘要:在某些实际应用中,采样得到的数据点处导数为零,即驻点。我们希望得到的插值曲线保持这些驻点。已有的Shepard方法得到一个有理插值函数,但并不能避免在恰当区间内出现极点。本文给出一种高效的保驻点插值方法, 且插值函数为多项式形式。最后通过数值例子以及图形,展示了新方法的正确性和有效性。
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Curve interpolation preserving stationary points
Abstract:In some practical applications, we hope that the interpolation curve has some special properties at interpolation point, which is the interpolation with stationary point. The Shepard method has been successfully used to solve this problem. However, the interpolation result is a rational function. This paper presents an efficient method for interpolation with stationary points based on divided differences computation. Numerical example and graphic is given to show the correctness and effectiveness of our method.
Keywords: Computational mathematics Stationary point Interpolation Divided differences
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