| 对二阶数值微分算法的一些改进与对比试验研究 |
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| 引用本文： | 颜青,张华.对二阶数值微分算法的一些改进与对比试验研究[J].河北工业大学学报,2011,40(4):51-55,59. |
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| 作者姓名： | 颜青 张华 |
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| 作者单位： | 铜仁学院数学与计算机科学系,贵州铜仁,554300 |
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| 基金项目： | 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) |
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| 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...
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| 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 |
Some improvements on the algorithms of second order numerical differentiation with the comparison study |
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| YAN Qing,ZHANG Hua.Some improvements on the algorithms of second order numerical differentiation with the comparison study[J].Journal of Hebei University of Technology,2011,40(4):51-55,59. |
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| Authors: | YAN Qing ZHANG Hua |
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| Affiliation: | YAN Qing,ZHANG Hua(Department of Mathematics and Computer Science,TongRen College,Guizhou TongRen 554300,China) |
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| Abstract: | 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... |
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| Keywords: | second-order numerical differentiation algorithm ill-posedness regularization the first kind of Fredholm integral equation |
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