基于切比雪夫节点的重心拉格朗日插值

Barycentric Lagrange Interpolation Based on Chebyshev Nodes

文章研究基于第四类切比雪夫节点的重心拉格朗日插值及其相关性质,讨论了重心拉格朗日插值公式的具体构造及其计算速度,推导其在加权Lp范数意义下的逼近阶,选取采样函数利用Matlab绘图并比较插值误差.由图示及数据表可知,误差随采样函数光滑性的增强或插值节点个数的增加而变小.

This paper studies the barycentric Lagrange interpolation and its related properties based on the fourth type of Chebyshev nodes.The concrete construction and calculation complexity of the barycentric Lagrange interpolation formal are discussed,and the error under weighted norm is deduced.Finally,the interpolation figures are depicted and the interpolation errors are compared by selecting sampling function and utilizing Matlab.From the graph and the data table,it can be concluded that the errors decrease with the enhancement of the smoothness of the sampling function or the increase of the interpolation nodes number.