近似已知函数的稳定求导方法  

A stable method for differentiation of approximate specified functions

作　　者：冯立新[1] 刘松树[1] 邢泽晶[1] 宫浩[1] 

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2009年第1期51-54,共4页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省自然科学基金资助项目(LBH-Q05114);黑龙江省教育厅资助项目(11511276)

摘　　要：考虑由扰动数据重构原函数的导数问题。利用积分算子,提出一种新的构造近似导数的方法,与Groetsch提出的求导方法相比较,提高了稳定近似导数的收敛率,在一定的条件下近似已知函数的导数收敛率可以达到O(δ67),δ为近似数据的误差界。证明了上述收敛率在某种意义下是最优的。The problem to reconstruct the derivative of a function from noisy data is considered. A new stable method for differentiation of approximate specified functions is presented by using integral operator. The convergence rate of the stable approximate differentiation is improved and the improved estimate is O （δ^6/7） under some conditions, as compared with the Groetsch＇ s method for approximate differentiation, δ is error bound of approximate data, and it is proved that such convergence rate can be optimal under some conditions.

关 键 词：不适定问题 近似微商 收敛率 

分 类 号：O241[理学—计算数学]