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| 求一阶数值微分的L-广义解方法cTSVD | |
| 引用本文： | 赵振宇,贺国强,窦志红.求一阶数值微分的L-广义解方法cTSVD[J].高等学校计算数学学报,2010,32(1). |
| 作者姓名： | 赵振宇 贺国强 窦志红 |
| 作者单位： | 1. 上海大学理学院数学系,上海200444;广东海洋大学理学院数学与信息科学系,湛江524008 2. 上海大学理学院数学系,上海,200444 3. 河北工业大学廊坊分校,廊坊,065000 |
| 摘 要： | <正>1引言数值微分也就是给定一个函数在一个区间或某些离散点上的扰动数据来求函数的导数,它产生于很多实际问题当中,比如,图象处理中的边界识别问题;Abel积分方程的求解问题;化学中波谱的波峰识别问题.以及一些数学物理反问题当中.数值微 |
| 关 键 词： | 有界变差 函数 第一类积分方程 扰动方程 伴随算子 方法 广义解 数值微分 |
CTSVD METHOD OF L-GENERALIZED SOLUTION FOR SOLVING NUMERICAL DIFFERENTIATION |
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| Zhao Zhenyu,He Guoqiang,Dou Zhihong.CTSVD METHOD OF L-GENERALIZED SOLUTION FOR SOLVING NUMERICAL DIFFERENTIATION[J].Numerical Mathematics A Journal of Chinese Universities,2010,32(1). | |
| Authors: | Zhao Zhenyu He Guoqiang Dou Zhihong |
| Institution: | Zhao Zhenyu (College of Science,Shanghai University,Shanghai 200444/ Department of Mathematics and Information,College of Science,Guangdong Ocean University,zhanjiang 524008) He Guoqiang (College of Science,Shanghai 200444) Dou Zhihong (Hebei University of Technology at Langfang,Langfang 065000) |
| Abstract: | In this paper we consider the numerical differentiation of functions with noisy data.We introduce the cTSVD method of L-Generalized solution to deal with the ill-posed property of the problem.Since the singular system of the operator concerned can be obtained easily,and therefore the method can be performed easily and fast.Theoretical and numerical results show that the method is stable and efficient. |
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