求一阶数值微分的L-广义解方法cTSVD  

CTSVD METHOD OF L-GENERALIZED SOLUTION FOR SOLVING NUMERICAL DIFFERENTIATION

作　　者：赵振宇[1,2] 贺国强[1] 窦志红[3] 

机构地区：[1]上海大学理学院数学系,上海200444 [2]广东海洋大学理学院数学与信息科学系,湛江524008 [3]河北工业大学廊坊分校,廊坊065000

出　　处：《高等学校计算数学学报》2010年第1期82-92,共11页Numerical Mathematics A Journal of Chinese Universities

摘　　要：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.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 ob- tained easily, and therefore the method can be performed easily and fast. Theoretical and numerical results show that the method is stable and efficient.

关 键 词：numerical differentiation ill-posed problem cTSVD method L—Generalized solution. 

分 类 号：O242[理学—计算数学]