对二阶数值微分算法的一些改进与对比试验研究  

Some improvements on the algorithms of second order numerical differentiation with the comparison study

作　　者：颜青[1] 张华[1] 

机构地区：[1]铜仁学院数学与计算机科学系,贵州铜仁554300

出　　处：《河北工业大学学报》2011年第4期51-55,59,共6页Journal of Hebei University of Technology

基　　金：河北省自然科学基金(A2006000004);贵州省教育厅自然科学基金(黔教科2008099);铜仁学院科研启动基金(TR051;TS10016)

摘　　要：基于Tikhonov正则化方法,对一种第一类Fredholm积分方程进行离散正则化处理,得到了求解一类带扰动离散数据二阶导数的稳定算法,它在数据的误差水平已知和未知情况下均可应用.基于Richardson外推算法对半离散正则化算法进行了改进.最后设计了全面、系统的数值试验,对现行几种二阶数值微分算法的性能进行测试、比较和分析.实验数据的有关分析和结论对于算法在实际工程中的应用提供了有益的参考.Based on Tikhonov regularization theory,a kind of stable algorithm for computing second order numerical differentiation of disturbed data is obtained by discretizing and regularizing a first kind of Fredholm integral equation.It is effective both when the noise level is known and unknown.The semi-discrete regularization algorithm is further modified and extended via Richardson extrapolation method.At last some comprehensive numerical simulations are presented in order to test and compare the performances of these algorithms.The analysis and conclusions are useful for applications in engineering and technology.

关 键 词：二阶数值微分 算法 不适定性 正则化 第一类FREDHOLM积分方程 

分 类 号：O441.2[理学—电磁学]