关于插值和运算的截断误差分析

Truncation Error Analysis of Interpolation Sum Operation

截断误差估计是人们在研究数值逼近中的主要问题,对近似误差的不断缩小和对精度计算的不断提升是工程问题上坚定不移的探索目标。本文着重以截断误差作为研究对象,提出最优化误差控制问题,通过对插值问题和数值运算问题上误差控制的探讨,证明误差控制的理论,达到优化设计误差问题的目的。

Truncation error estimation is the main problem in the study of numerical approximation.The continuous reduction of approximation error and the continuous improvement of accuracy calculation are the unswerving exploration goals in engi⁃neering problems.This paper focuses on the truncation error as the research target,it presents the problem of optimal error controland proves the theory of error control by discussing the error control of interpolation problem and numerical opera⁃tion problemso as to achieve the purpose of optimal design error problem.