Stable Lagrangian numerical differentiation with the highest order of approximation
Stable Lagrangian numerical differentiation with the highest order of approximation作者机构：Department of Mathematics Zhejiang University Hangzhou 310028 China Department of Mathematics Zhejiang University Hangzhou 310028 China
出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)
年 卷 期：2006年第49卷第2期
页 面：225-232页
核心收录：
基 金：supported by the Special Funds for Major State Basic Research Program of China(Grant No.G19990328) the National Natural Science Foundation of China(Grant No.10471128)
主 题：Lagrangian numerical differentiation truncation error stability saturation approximation superconvergence
摘 要：Some asymptotic representations for the truncation error for the Lagrangian numerical differentiation are presented, when the ratio of the distance between each interpolation node and the differentiated point to step-parameter h is known. Furthermore, if the sampled values of the function at these interpolation nodes have perturbations which are bounded by ε, a method for determining step-parameter h by means of perturbation bound ε and order n of interpolation is provided to saturate the order of approximation. And all the investigations in this paper can be generalized to the set of quasi-uniform nodes.
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